Maths-
General
Easy
Question
QUESTION 12: A square has vertices (0, 0), (m, 0), and (0, m). Find the fourth
vertex.
The correct answer is: BD = m (Since ABCD is a square)
SOLUTION:
HINT: Use the properties of a square.
Complete step by step solution:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM8AAAC/CAYAAABZo4ieAAAUk0lEQVR4nO3ceVxVdf7H8fdduJdV9kBBUUsENTG3xA3NQWnRpsxmrEyznNKsmTQntSmbKbOaycn62TJjWmpii3tm6fzU3LcyyoXQlEUUhcvlwgUudzmf+QNccIUvi9q8nz18PLrn3rPBed2z3HPRiYiAiGpNf7UXgOh6xXiIFDEeIkWMh0gR4yFSxHiIFDEeIkWMh0gR4yFSdNXj0TweNOwtDgKPR2vQOVBD0OB0unAt/+aM9TIVcWDXph3IsxXD188fN3XsipbhTa442u75E/HarlaY//Z4+OkBoBR792xGznEX/FrehL4d4+FV12XTSjH76ZE41nMq3niwS12nRjUgbhu+37gDJxxOaJrAaAxHbMd2uCk6sEbjH9u7HBNemIbDxwUFfkEY9+eZmHBnV5iu+lv9eaSO7FlpMmbYAGndvIP0v22AJLWPlh73PCF781yXH1E7Lk8O6CJTU9NEExEps8qb44fKjW3aSXJydwmIaSGP/mOlOOu6gKLJ5vfGys19npKTdZ4W1YTbtkWS9H4Sn9BbBg1Klvi4G6Vd++4ydc56cWtXGtsln80cK5PeWCK7d2+TBa/+SSL82siivQWNsei1Usd4iuTl2ztITMp4+TmvXDweTVyOUvnh4I+SVeC47Jj2vR/LrYm/kS2nKh8fWDRe/FsmyfpfbKJpbtn76TSJDIiWT34qqdsiikjFL6uld+fOsvBHe52nRVfmLtok/Zt1l492HRdN06Siokh2fDhewgyh8uqXB648vsdz9oFmkaeSW8jAl9c04BKrqdOOsGD7fLyb5sYrL7+E2Ahv6PU6GM2+SIi7GS1CjSgtKYTFYkFhYSEKCwthsRTAVmIHAGxdux4IS0T7MACw46vFu9AjeTh6tW4Cnc6AToOGoXMcsG7bwQtnXLgPE//4OD5f//+Y8sSd6JfYCy/M3Yi83O/w+rjhSOp9G8Z/sBZ2d+XZlKlVJyToNaxfu6OBz6/oDB2gN+ih0+lgMgXi1tEz8fLDN2H2nOWogMBRVnTetmGBtcgGjwAG/Tmbpc4IXz8veBnr5wyjPtVpidJ370JQy/bo0SH0guc8pfsx5Z5HsOGkC3q9DkDlxYHmtw7BovemI/3wYVTEDECQDoBWgtxiQXhia5hOTyAwGDc2CUf2sRMXzthtx+51n+KDTZl4esxIjLphIyZMGIYlEdFIfmwUHom1Yfq0kWjWcgemDooBdM3QtZsHczP2w4EB8KnLSlONSbVvu3ihS7+ekLH/wT7HGGx/egQ+2HkM+qpQRNPg17QN3lmwFF0jAIjAYy/B96vnYMnPRkx/ofNVWYfLqVM8pXYXzIYwmM0XPqf3boNJs1Px5Hnv9UafJvDXrDh6LBNNe4VXDpQKlLgqoMk511YqDykvOW+nORyjJ7yOV0d0ApCEb5cug3PEq3hr0u3QwY6sbauwfU86MCgGABAW2RSFByxwaYDPtXbi+T/C5OMHHzhQWh6E+5+fjWSnq9rzOqMJUSGV/1+Rux5D73gWjqiumPLeMtzfOeQqLPHl1Skeg0FQUn4C9jIAftWf0+nNCG8efcGlRp3eCD1s8Hjc8DadvpamO/PfucRghHdgwIUzFoHZxw9xrWOqBgQjIsoX5RHhVVNwwWAwQ/N4zoxiMvvAWlwClxs4u3ujxlRWXIRyUyRCAw0I8m4K//PfHHV6mKu2SL3JjdySALz5wXu4rcW1d8gG1DGezn37oOjvs7HrQAHiu4VVe07K9+HZO0dhY4EbVUdtEE1DdPchWDDrBfh6+8BWWlb5hCEErQL1WJN+EA4MhDcAWPORYclBu+bRF5+5CDyn4xANmibVYhER6HRnYywvtSI8JAgmhtNo9Oeeu0DDnk0bYbrjMcTpSzBr7P2Yuyf3zCG9iAa/yDZ4Z+EydIsA9L4xGD5yKKJ8r92z1DrFE9LtATzR7U28MGk62rw7GR2ifeEusyI9/RCCY2/B8x8vxpNlGvRVG7FoGrz9gxDmb0Cr6BvxTU4eNAB6BGDAPV0w/YX5+HLPPRjUNgBbF89Fem48/prcBoCGTR/8FfN2eePlOVMQXevDLgcy0vIR3qIpdzqNRdNQVlwMu90HZWWnsO2DF/HGVsHrn9wPA5pg5Gvv4nars1o8Ri9vRFe9B7ssJ5DxSyYybHa0DQu+iityaXXbHxpDMOXfi+H881MY0q8doqNiYCwqRHDvBzD9tZ6IbxGLppcYNeHmWLje2YBfXGPQxgvoPuJlzNjzACb1ScRr7f1gK22GKfM+QmIwAAiy07Zi80/tKhdYBC6XC55z3pQ8bhc8mlR77D59Z4EzC7t/1iHurgRc5PSM6pveCIMlHTNG34M5oWbknrKiZYdOmDkvFcNurdwiQiNbIzTy0pNwnjqI+QuXIG7cRAy+8dqMRyeXOyuvKSlCxqEs2O0emH2C0LJNa/hdIcuSfcvx6IwlGD/jQ/RtUbU/8JQiO/0wCio0RDRrjajIqk+kKyz45+QxcPWbgT/f3RZwl+FIVi4CI1sh1M8IQEPe0QxoQS3QLNgXgAencrJQbg5HzA0BqMjcgLEvzcWIv85D/5hr8/j510S0MmSnH4HV6aq8w8AUgpjYFgisxS0C4izG4SP5CGnVEqFmQwMurbr6iYfofxAv2hIpYjxEihgPkaIGO3s+duwYbDZbQ02efoVat24NH5/r6OaphrrjdNiwYQKA//ivxv927NjRUJtjg2iwwzbjNXgXLF3bzr0j5HrQKFu42WyGt7d3Y8yKrjPFxcWXvQH4WtYo8UyYMAFTp05tjFnRdcTtdiM+Ph55eXlXe1GUNNqex9/fvzFmRdcRTdOuu0O1czXKperrdbdMDUvTruW/jXNl/JyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSBHjIVLEeIgUMR4iRYyHSFGjxGM0GhtjNnSdMRqN0Ol0V3sxlDXKVv3+++9j1apVjTEruo6ICPLz86/2YihrlHhyc3ORm5vbGLMiajQNdtjmcDgaatL0K+XxeK72ItSKTkSkISa8detWZGZmNsSk6VcqJSUFoaGhV3sxaqzB4iH6teOlaiJFjIdIEeMhUsR4iBQxHiJFjIdIUaPGIyVH8FnqMhy31+90rRlbsXjVVpTX72TpanDkYlnq5zhibdgPTLN3f40lG/ZBq8M0lOLJ3fIh+iYk4C/ztqLmHxIJdiycgdc/3giPV+WQkuy9eG5cMvr06YWOdw3Gvzen41I/Mq3Mhk9mPYG+fXqiW58eGPfeZyh2Vj7n5c7GK88+j42HilVWh+pR7neLcVenrujTpy/69OqN3gOfxZq9x2u8kR5Y8Q5efncFXF51f193WnPxz2nD0LtXL9zSPwnTvtgIR9WCeAr34pnxf0N6kVt9BlJrTlkwKUVuCA2RsJTnxOKq6WgnZeKQLjIxNb3ysfWg3Ne7o/T5/QuyevVK+ceUYRIY0l4+/6HgwnG1Mpk3+T6J6HCvLExdLqkLX5H24aEyZuZ/xFk5MZmc3FYe+2BL7VeH6tWhdW9Iq4Ae8uHyr+WrlSvkuXu7S1jrZNl2wnnlkbViefWhHjJ69s66L4jjpPzlgSS5sd8fZOmylTLvnT9Js4BmMn3ZARER8djS5XcdW8j0dVnKs6h1PFpJugzvkSgzP3pbukbcIksOldRovKL0L6VvXCdZcaRCREQOfDpZbmqTKNsLq17gPiVjEgOk/7SVF4zrOLFTftPcX15ak31m2OoXfyNNeo6SHHvl43X/HCGx/Z6X4tquENWrw+v+LvGxD8qR0wMOfSHNY2Pl/a0XeVM8T3nuVhkUFysf/WCtHOAolJ07d0hRWZns3/6lLF+5SjJOlIuIJod3bZLlK1ZL2snSi04r//tFktC0qczffzbatx9qIy1+96o4NBERh7w/tr/0GjVHKhTXtdZ3VaevnYeffBMw677RKF49B58v/x73PtsXQDm2Lv8YG/YVQK/Xn96rwRwQigfHPAHb/m047Ncd3aNNAICf9x1FYPMUtA+umrAhGD0TE7Eh7QAcGAzvc+ZZfGo/jtm6IOmW8DPDOvcbBN28b5Bjq0C0nxltb+kB/7cW4PvCV5AUorofpnrhcsJeVIEKbw1pm3ch4oaO6BoXDMCJ77/+BGv25EJXtY1ABHpvf9z/2B/hc2g7fpQEzGoZWPmcdT8mjRsBtE2C51QOnAf3IT92EB7pqseWXQdgzStBrl8HpC79GEkxvtUW4cTRgyj3ug0947zODLu1/0DYZh1CvguINpnRtevNeH/2OmRWPIpYc+1Xs5bxlGBp6ma0T3oe4X5+GDwwCUsWLsTRcX3RyteFvIPZOHr0ZLUxvAJLYXMAxzL2ozQ8Dn56AHCiqNgGVxNveJ3zWrOXGV7l5XAB1eJxWCyw+plRbf1MZvhWuFBedSducFgzeAdmIfe4ACHX7xesrnc6ownOo//B6JQBMLrLkPbdAaS8shCdQvQA3DiZkYMjR7OqjaP3DkBhGWDI2A9bWBMEGKt+f3ojKux2uP06YtWKuQi3bUZSu2R8YRqHRcs2I954DKNvvw0ffvUTksbeWm2a9sJClAZ6w6ThzJm90WSGb7kVjqoT9YjoSLh125FvBWIja7+utYrHmfMdNhy2IOXxDrBYLIjq0g3atBn4es8xjO0bjaFTXsXQS4y712LBDYEBMBgqH2uaBrnINq43mWA4f6CmVZ5wnvN6HQAYjfDSVw708Q0A9GbkWywAwmqzWlSfPG4Yo2/BU397ETFmwPrzWkx4cTJead0SLw7vituffhG3X2LUbwoKEBTQGl6nt0rNA31QFEaNHIWmvnrAJwHdb46A4eFH0SHYDCAUN0U3x06L9YJpiaZBu9h7qMkLp9v0bxIKp1uDtdgJRJpqvaq1iid913qk7T+BIxPvxgJo0OnsyD2eiTXr92Bs3zCsmf02NmZbqs/APwyPPD0JXgYdPGdu4DbAz8cHKCiGA2f3MiVlxfDcEIbqO2DAGBAAX1sJyjxnr+257TbYgpsgzLtypUUEeh1gMinsf6neiGjQ+zRFn+QktNIBSErCqR3LMXPlWkwZnoDtH72Lrw4erzaOzuSHB55+ESaDHtp5N/kbdDj7ZioGGE2A01lRNUCDR9Og119Yibe/P0z5mSg756kKexHs4SEINZxeVoHBoIeXUe3KXi3GcmDdklVInPgWvv5sMT777DN8+ukazJs5Gj8tXYoslw6mAIHT6YTb7Ybb7YbL5YJoHpiNQNOoGJy0WOF2A4AB7RLaoPDoSuzMqbp2WJ6Ftet2o2+vzgCAMksWdn67G5YKIKh5R7T034MVG45WLYtg3YqViGkTj4jAyp9EUeEJVJS5EBYSoPSDoHpUbVt2o6i4DJWbmgGmAIHrnG3E7XJB0zwwGYDIqBgUWW2ocFWfnJwJSnC5L9DkH9mHXfty4AQQHXszfB1r8fVOW9WzDny1/Bt06dIJvlXx5OdlQy9GBAWqfaG6xmNV5GxA6jYNf5w4BLFtz35hqZVpGGa8NQKpm6yY/PBzGPDwJcZv2wGR+7fiaIWGBKMe7e94FAP/tQTPDB2Ox35/C/ZtW40ffUfj8yE3AwCyt8/HbwfPx7+O/YzBTbvgD4+n4JnJDyHg4P3Qe/YhdaUZz8wdi5CqNcjLOoxia0fcFKP0c6B6IhDYD+/BnDdmIdLXg6xDm7Foiw+eX/B7eEGPxKF/QuIlju3z2nZA9C+f4IjdgWh/b0A8cJSXw+U5G4/TUQaXWzvz2FXhgMMlADxY9LcReGZzOxw4+AniOtyBh4a8gzdG34PSh1NgObYJy37uhrf+MbhqTyY4ciAbenRCVPDFlubKarznOXEkB31GPojb2lX/pp+pZVc8/odH4FN88hJjVmoe1xMxAXuxZX9R5YyD4vDu4qUY19UHe/akIbDVXfjqm1lICK087Co4noUb+t2NbhF6QO+NB15agAXPpCAnIw3Zuf74vyWL8OTA6DPTz/jxO/gOTEFH74vOnhpJYFQC7v1dF2Sm7cKOHXtgLW2Bfy9biSeTW+JKl3HCWyWifcQBfPvjqcoBvpEY/NuhaB9Z9UvVmdDjzgeRGHv6nNaMzgOGYFCnKAB6dEkejvGP3o0wLwDeoZj6/hK8eV889v/0A2yeOKSu/QhDOlSVopUiLf0Amt91J6JUP49VvMRde85CmT6su9w9+QvxXOGlnpIf5f6efWT2t5k1nHamjOrSVv6y5Kc6LyZdRZ4yee/xftJ/zL+UP3upKUfeNhnQqq3M/T5feRqNd2+bVzCGj7wDuVuWIaPk8i/1FLkw6MnpeLRvzY7BCnZ9id36BPy2b2w9LChdNXofDH34PpSnrcDe/Ia9ty1j/TLktL4DKfHqfzOhcf+GgacMmVn5CG8eAz+vK7+8phxFecizG9AiOpy3iV/vxIHszBMIatoSTbwb7vO6klM5sEoTtIgIVJ4G/wAIkSK+URMpYjxEihgPkSLGQ6SI8RApYjxEihgPkSLGQ6SI8RApYjxEihgPkSLGQ6SI8RApYjxEihgPkSLGQ6SI8RApYjxEiv4LPfx8jTIOeDIAAAAASUVORK5CYII=)
Here we have ABCD as the square.
Now, AB = m
⇒ CD = m (Since ABCD is a square)
And, AC = m
⇒ BD = m (Since ABCD is a square)
So we get that D = (m, m)
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Maths-
A square park has paths as shown. Use coordinates to determine whether a coffee shop at point M is the same distance from each corner.
![](data:image/png;base64,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)
A square park has paths as shown. Use coordinates to determine whether a coffee shop at point M is the same distance from each corner.
![](data:image/png;base64,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)
Maths-General
Maths-
Place a scalene triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign
coordinates to each vertex.
Place a scalene triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign
coordinates to each vertex.
Maths-General
Maths-
A gardener buys two kinds of fertilizer. Fertilizer A contains
filler materials by weight and Fertilizer B contains
filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?
A gardener buys two kinds of fertilizer. Fertilizer A contains
filler materials by weight and Fertilizer B contains
filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?
Maths-General
Maths-
State and prove the Midsegment Theorem.
State and prove the Midsegment Theorem.
Maths-General
Maths-
Find the midpoint and length of each side using the placement
below. What is the advantage of using 2h instead of h for the leg lengths?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUkAAADcCAYAAAD9VlPsAAAgAElEQVR4nOy9d5wlVZn//37OqRs6T+jJM8zABBgYgQEGJCsqSRBBV5Swsl9X/a5hg/paf+sG100/13Vd428VlWwAQQZBECVnGIICCkiOM8Pk6el0q855fn+cqtu3wzQDTmzPe149t7tu3bpVdW996knnOaKqSmS70dvby2OPPcaMGTOYOHEiIoK1dkfvViQS2QxmR+/AWEZVB/0APPnkk3zhC1/gnnvuwXuPMfEjiER2ZpIdvQNjHedcXQxVlauvvpqrr76alpYWDj30UDo7OxGRHb2bkUhkM0QzZhtSiJ8xBmMMTz31FFdddRUA11xzDffee2+0JCORnZx4hW5DVBXvPSKC955rr72W3/3ud1hr6erq4tJLL2Xt2rU7ejcjkcgoRJHcxogIxhhefvllrrzySrq7u+vxyRtuuIHbb799B+9hJBIZjSiS25jCmrzwwgu5//77gQE3fOXKlSxdupTe3t76et77Hbm7kUhkCDFxsw1RVYwxdHV1MWHCBD760Y/y7LPPcvXVV3PMMcewaNEiZs+ezapVq5g2bRrWWlQV51wsC4pEdhIk1kluW9I0RVUpl8sAXHnllZx22ml89atf5a/+6q/q2e/CLYdgacaMdySycxDd7W1I4UIDwx4L8YQgisW68Z4ViexcRJHchqgq1tp6drtYBpAkI0c6CssyEonsHMSY5Dak0YVudKUbn2+MPRYxzOhqRyI7D1EktyGvN7YYY5GRyM5HdLcjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJSCQSGYUokpFIJDIKUSQjkUhkFKJIRiKRyChEkYxEIpFRiCIZiUQioxBFMhKJREYhimQkEomMQhTJN4j3HvUKXvFZP0r/iOspigcy1XzB4EfdDvsaiUTeOMmO3oFdE8VrhqhgVMiyDdx260386Ee3sbFnHULGrKmzOOH44zjosEMoNbXiHDSXE9Q7AEwukl7BCMiOPJxIJLJZoiX5BhFjAEEMGAt333MHt9x+J5WmFsZPnMDa9Wv5wr98gY9+5KM8+shvSUo2WI11NYw2ZCSyKxAtyTdEUDrFo2rAOQzCwYccwn/913/SOaGZng29PLDsPr7w7//Kl7/8Zb705a8we+okNNqMkcguRbQk3wBKiEk65xEEMRZVBfWoehRoamri6KOO5uP/96M8+sjD/ObhRwAQYwdvLGpmJLJTE0XyDSAoIpAkdojICSqCAIm12FLC/vvuR3tbG48//gQZ4CW3QqM4RiK7BFEk3xCCMRYRASQ8SjiVkougGANZxviOdia0d5D2Z3jA51vwUkQlY2wyEtmZiSK5LTGGvt4e+np7sNZgGBDJgB/5dZFIZKchiuS2RODZZ55m44aN7DZ7NjBQJjlgQcZUTiSyMxNF8g9CCGIniILBUTIGS4KIsPbVVfzgB5cyafJU9t9v37yUoMiMK4JHVINcqoJqvfjcEexMRUGLvyKRyPZmzJQAqSpbIiQiob5xVIrNSONjELDwG3gPqCKieC1DVuX5J+/hyh/9gJaOdro29vCrG29h+ap1fPIvP8H83SdjfA2SElBBfQnvMrxaEIN4hxHFGUOGxZlwB6tohvgMTKke94xEItuPMSOS2z4BUliN4X/1YYmIAW/Ya699eOD+h7n8sstQY+mY0Mmb9j+Qvz7hZPbdZwGWflSFLlfCTtqb1a6V9ZRpsUIpq0EujiJCoo7EpQgGFUtqylhMNPsjkR2AqOqYSK+qBuf0tdgiS3LoZqRxce4OZw4jgqhHsxpZVgMRxCR4BbElknIJ74RMlZJNqdWEz17yKy67dhnzp0/gPae8hRMP2Zu5LQoYMgwlHNb3INoPpkRq2+gXSwUovb5TEolEtgJjyJLcmmxGJRt+T6wlrdVIjEFsQslajLV1V9wYS1brRVCsbaLmodvDulqCtE3j1Z6U86+6k5Vr+jnj7fsxe6KlkqYYehFSEItKCRCSfHx3JBLZ/owpkfTeIxLqFlW1/reqNtQ0KoUIDn4uEMKPecpEZFDVtyJ4VbwqiRGstSCCc4rJx3J7r7lIKkkSNpWpx2FCIiYp09u1iXccuSe2Yrj25mU8tWIjH3n3wRy2WysVb/GS4E0Zj8WSu942ARkyWicSiWxzxkyYqxBF7z2qiqqSJCW892RZRpqmpGlKlmWoKs45nHP1dQeiDop6h/MZWVbD+QznHGkaHl0WhiM65xAJQmlsglPBiw1udilktwWwtkSpVMKL4BWsOmy2iQWTS/zNB97KiUct5tFnVvDli2/k5w+vZAUtdJsmatgwxDGroVojFp1HIjuGMSOShQVZ/CxfvpzLL/8JK1Ysp1QqYYzBGIO1NgibMXVBLZ4DyQXT4VwGqhgTEjbWJhSja4wxoLBq1Sq++rWv8+Qzz6BicAg+NzwlF7UH73+Ayy9fSlqrYY3FqCPRfiouZd64Kh879RA+9K4lrNuwnq9eegs/vOs5XuhVaiiiDrEGb8ro2PmoIpFdijHjbhcus8td7FtuuZmrrvoZBx54YP25devW8pvfPMLLL7/MhAkTOOCAA5g2bVqe9AkC6DX3sAU2bdrEk089ze9//xRgWLDnQvbdd1/EGkSENWtW87WvfY0FC/dh7vx5eMJdp3DoxQhrVq/koosvZtq8OSzce/9QC+k9iVFKZMxsNpxx1DymTaxy/s/u43uX3cDKVxfz/rctYv74CqWsRiIKEoOSkciOYMyIpPceNMQUszTllltvY6+FC5k+fTrGGFauXMEXv/gl7rjjTowxpGnK/Pnz+fw//zP7vulN1HPXqnjv8N5x7rnncu1119Hb209PTw3E8hcf+zjn/NkHsYngXIaxCf1pRuYUY4tCcQCBLGXxvotoaypzz513s2DvfVGb4BHUS14f6ZlcEk7afzcmtbZw0bX3cM1N97FiTRcfetcSDphSpex7ESwDH1fhejcK50jLIpHIH8qY8eFULIglMZ7nn3+Mx556jn0OPJBSuYSr9fCDiy7ikd8+wde/9U3uvvtuLr7wPLo2vsr5F1xIV09GJoIjC+50UkVMiWOPfQff/+653HrzDVx11eUsWDCP8y++hJdWrkaNoUxK2VhsuZVmK1SBMo6aenoceFNm/ORODj5gX5546D6Wr1mDN1XU5A14VfAYjCpV9Rw6fyKfOv0ITj58Ab/7zYN8/eJrufaJVbxoW+hVgzpHlqVkrhfne/GqYTCOU9AeoLZDP4NIZCwyJkRSqY/qQzTj/vtup9rSwe577oUH+jZu4LZbbuGwI47msMMPp1qtsviAfTn+uLdy/wMPsGL1WrwoDoeqoGJJylUWH7CEeQsW0NRcYe4eczj88MNYv2kjvVkvqToSzUhU6aul/OLGO/iPf/sXfnThuby4Yjl9CplabLmFvebvzqMPLePZF17AVqp4SUK8UxVvLJiEkjFUgYVTO/jIKYdxxvFLePmFF/n6D3/JT+57jpf6PZsQnIKvKThBNMVLPyoZ6hLwMfsdiWxtxoy7LQYMAqosW7aM1uYWZkyfgaqybs1a1q7dwG6zZ1MSg6t5bNkye87urF9/DevWbmD3OVPCwEPV0EhXAbK8HAicczz3/HO0t7fT1NyGCBgDXpVLLrmC/o0r8f1ruPSl5zjk4Wf5/Oc/z4S2JiBlytROammNF19ajtiZ1F1jBVHwXjECVkBFmNTaxPtOPJwJU6ZxydKbuOTiq1n3ymGceex+zKgK7UkF4wU1/WD78VpGaEZik8pIZKszJizJAhHwtYw1q9dRqlRprraQmISuTV14n5KUgqUlRUF4EmbgSp3L44TFeBqoC5kImDL3P/Agy5bdz/HveAdTJ00g5FIsvT09dHS08dWv/TfXXPsz/vqvP8r999zN008/lyeMlI5x42htaWbFipXBUiWIukg+5tw70AzUYdSTOKVZDMcePI9PnX0CC2d2cvn1v+Grl97FU2s20WM9zipQRXwrUAbjUIlNMCKRrc2YsSQVxakjzfrp7eknGVciKVm8+jwZM5B59niMd1hbAh86jDv1JGJCN1yfC44AYlmx4hW++a1vMmu3WZzzZx+kkljEB/++qbmJk971TubOnUVZ+tln0UKaW29kw4YNxY7R0txMU1MTfb09yLiwP9YaxBiMgjFST7cYdUgu2IkkvHnhLMa3H8vF1z/Mbff9lq4N3bz/xAM4fM/JdHgoOYsYgzN9CAZLecd8AJHIGGXMiKQAiJJYi0gJ56ReizNhwgQq1RJ9vT15wiRYXN3d3ZQrJZqqTaj3OHX5FLEZqh4pl1mz6lU+//l/Zv3GTfz9P32e2bvNJHVKkvcE8gqlkkVQvKYYA6Y+rYOACGnm8N5jjEURxJh6wzQjBlMv7/F50wyPsQYnHo+w/8yJjD9tfyZ2tHH5rS/x/I8f5cPv3pOTFk5mAiniyvS7MqUkuOyRSGTrMbbcbZRSpUprWwv9vb309TlqaUpLSyudEzt44snH6entJqmUyNKUBx94gFkzZ9DZOR7vPbX+Xpxz4DyJNaxZs5r/+H+/yKO/fZwvfOFfOeTAg0KTCQEjgvcea0G9I/MewWNKoYYyn14bEDZ1ddHT083Ezs6wZFjN46CebAiCESXBUcZT0ZT54yp8+JQDOefMw1nXW+O/vnszl974KGtST1Y2ZFbwOqY+zkhkp2CMXFWK4lDvQGDu3Dn09vSwdu1arEloaWvl2GPfwe233c6FF13Mffc+yLe//W1uuukWTjzxBMZPaMMYy9KlS/nud7+L4snSlG9/+ztcd90vOPOss+mrpdx13/3cdf8DLH/pJfCKESFNM5TgPqMuxBm9y8eIh317deWrbNjYzdSpU7AiDDjXhbEbqtcVg2JRMYQ0lCAE61ZcmQk24z1LxvO5sw9m5sQ2LvrZMr511UM8uqqf1EoskYxEtgFjxt2GfKSMeo466miu+tV3ePaZ59lzxiRELe99//vooYkf//jHnPut77LXvBn85V9+khPedQqJhb5axm2330H32l4+/KFzWLN+LQ899BDr16/n++edR/qd74YyI4Gzzz6bT37so9hSQufE8SSJwfsM8mTMuPHjKZVCbFDV8exzLzJl8hR2mzGdu9Z057FODSVLQDHLIjp0cjCPAZxAzRgS389umjJpz3ZmfuQYvn3lMi676zmeWdPPh04+kINnTyAqZSSydRkzIikqZE6wpsS++x9Ee9sFPPrrB3jboYuxWDo7p/GJj/0FJ514At0bNjFlcgczZ03FaRnn4Lknn2TFKyt590nvptrUTKe1/NeX/ouNG7tJfTFsMdRidk6aRCkpMXXWHnzvgu8zcdY8LKBaYv6ei/niv+3FpM5poJ4NGzby4MMPc8SRb2XObjMpPfI7UCEjweOxmEHediGaQShN3dLMjFCiTDmFcuI4YEYbH3v/ofz4hse57bb72Lh+JX9+6ls4fO9ZtBsl8R68DbMyGlAcVhURW59VZ+gYHWmwa2MX9EgkMCZEUhAMBmtKKNDWMYU3H7QPD9x9K+tOP5VJnRPx3lO2hoUL9mx4pULmwNW48fpfMnfOXE477VQwCZVqwtx5e27uLUMZT+sEFu4zoWGJpaW1lb1b80U+5ZlnnuHpF17gL457D+Nbm2iyHtSQSYKKYvDIiFGPQrpsmMcbEJOgJUGkRrP2sWhCwl+ctIhZExKu+MUdfPHHN3L6CYdx8oF7MCMREpehEoQWMaQ+Q3AkNqnvcf1Y6u/a+FckEhkz5oJq8FXzyhxOPOEEpk6ZzOrVqxBjBgShoTWaakiiZFnKQQcdxIf//MOMGzd+i95vuIwIw06nGF555RX23HMvFi/eD58RCsjFbEYYR8YolH2wDoUUwWHJaPKemS1l3n/0vnzifcfRVhXO/8lNnH/Nw/x+g6MvcVjTReJrmExwkuCtpYiEGjwmj4QOHM/gvyKRP3bGhCUJ1FuYZVkGwP77789uu+1Ga2trvbFuIY5Ds8vlcpkjjzwSyBtlbCVUlQMPOIg3LT6IyZ2T2WgUxCMmjLCRkYR1pGPDYzWlPn+iCEbDlA4JSlNJOPWgecyZOo7v/PRufvLL+3l65Sr+73sP5YApTTQ7zVu0QdFQKDj0warNT2Axf2OeRopEIjCGRBIGBM57T6lUYsaMGXgfGuQCec/IwRTNdremONb3x3kmTuxEymU0DSVDkgtdvY5yi1AgC+ubIgMexKzkHGWvNCscvlsnHR94K9+7/m6ue/ApVl9qOfuEJbxtXjvjfT9VD+IMPgll9cG1doQ+mqErUbQiI5HBjBl3GxjoFG5CrWLRedxaO6ghbyNFI97NPf8H7Q8GY0t5l3SLGAnzbRvJY4Wy5Q3HxeKNJaNMJqXgOpuBUiHEU0ozFk5u4q//5Ag+cNwSXnplLf958c386N5nWaEJNVPGYag5JfVQc57M5YXzg3c8EonkjClLciRLscDafNz2EBHcmqI4CAWTJ0iKBLbxIT3uvYPXkSBRCfFEDVWT9eW2PnIniG/qwSrMrJT5+Nv2Y7eOZi76xb1ccMVtbFp3IKcduZCZrQlWPThHWSy28L2lwYaMuZtIpM6YEsmdH0VEB+bhCYMUt+B1gsfWtcvksUUjecNyI4DFWUOaQpOHGaWMMw6ZxdzOKv/fTx7gR0vv4fnVG/izkw9g4bhmTGIQHyRX6vHRMeZaRCJbgSiS25yi5jGIUVK2oQQxt2B1C2dmCCkVxXoNyZdi2ybMq+MRjHeUBVSCWLbbMm/Zaw9azprAeb+8n1uW/Y6u9a/yf45dwn4LZmGMxXnyDHckEhmJeG1sZ0qmhDUhBlqkTraEPF2TF+h4wIdGHXmzDgFK6qlYD4kjswmZryA1WDyng0994Aj+5Oj9+P3jz/ONH1/PDQ88TZeHzIQkkNa3GaoD/JCfQQzMyhuJjHnGjCW5zWKLfzBBfhKfJ3LUIpTQfOTLlvSkEARLXt9Y9HsbeBKTj8wRW0JRSkDJGvB5nNE55rdV+PQJi5k5vp0Lbryfr112C6s2ZZx06Dyml4VmVcT1hf0yZvCIm9zPN9q4QEP50M562iORrcSYEcmdkiJ5nYuLqS8MlYivb3RLQ/XiCC8Z6B80EOVUExJFVgS8Z3zZcvrRCxk/qZ0Lrrqd7/30Vl56dR0ffPti9hxfomQUJyVUhBI+xAKKLevAEURljPwxEUVyDCOAa3DHQenQGifuM4XJLW/jez+7m+tv+zXr1nVz5vEHsf/sDqoKZc0Is4iTCzpDAqdhjvKolZE/BqJIjmGK+Xq8+tAuwwiqUHEph+8+julnvZULf/Vrrrr7aZ7ZoHzwhP04YZ9JdBrJ58spMkQjjPKOAhn5IyEmbrY3Grpfbs8Yar3A3hicKWFsQrPrYe/xnr869RDef9KbWb62j2/+6Dauuv0JVvdk9EmJmiZkmue+FcDXowU+Jm4ifyREkdyOhKkZitIfrS/bZu+Xj2cvHkGwCFYMiEXUM6UqnHPMnnzmTw6iLcn4/hU3cMEvH+L5jTV6jKUXQ68zuKKbEB7U1bPqkchYJ7rb2xOBpJTUUzY74O1J1IEqTppRE2ouZ0iNMw+cwu7tx/Ddn93ND3+5jJdXruH0E49gwawOEu/xmdKcWASH4Ovd1KPfHRnrRJHcziQ29Ic0Ijuk3FDU5dU7lkwMVpXE1Ug05bB5E2k64+2cd83d3PTQY7zaVeNPTz6ExfOmUbEJXnxDfrvY+yiSkbFNdLe3A40yIiKoEcTkJ1+3s1Dm8+cYDeO8BcGbCs5bTJaxaHIzn/yTo3jX8Ufz3Io1fOOS67lp2ZOs73d5vluBFNTnY4AIpUKFC67aIP7RJY/s+kRLchuhQn1sdpILoc3VMEsEb4LgbPfWZJKAzcd9kw+atCWwJQxQRlk0zjLpHXuyx6QWvn/1fXzpR/fw0ppezn7LPsxs8XjXj9MyXiqU1GN8P4IjjB+v4iXMH240RaQEYrfvMUYiW5EoktuQwhkVLWasCbg8Q7xDInoy/NcimVRImXplesVy2pLd6ZzQwbk/u5Vzf34zz6/bwIdPXsLe7a1Uag4xiqhDNEO9xydlankBfT4NGsGajCIZ2XWJIhkZRk0NzkG7zThuQTsTzjyS79zwa5Y+9Cwvd3k+feJ+HDJ9PFUc4EJJkFiyfMYeIG+ZkRedRyK7MFEkI8MQAx4lUUezOg6e3knTSUcypfUxrrnxIf5tzXrOeddhHLPnJCaUSuCUUmJIDIiEKSHCOO9STO1Ednli4mY7Unev8/l2dtZOOkYyrK3hrMXRRHMGB3dU+acT3sRn33s4yzes598uv51L7n2el52lxzbhxWJdL+Wsm7Lrw6BksQlbZAwQLcntiUCpVEIAr3nH3J1QKA2eEkomYQR3Ig6TdTPRKGccOZemCe2c+4sHOfent/LKytWcccyb2HtCmcSlGGpACVUhNZW8S1EksusSRXI7I7k2GlOMwNnRezQc4xNM3vncmxrYDI8HDBV1vGvvaUxtOpTv/erXXHfjMjatepVzTjiQA2Z2UBVb7+ZmZHNzikciuw5RJLcjQRQNiOTNJhSvgt3JdESlaOqWkvgaXoTMVPEkGAztLuMte7TT+f5DuajdcMs9j7J2Yw9nnXwUhy3opN16ygLGZxhJiLZkZFcmfnt3AILB7qChiVuCx5FKLViPWkZclSSrkPgElyp9pBhT403jLR8/7Sjec+rx/OblGp+/+A4uf2g1KzJDvyqJcXn95NAjja3NI7sOUSS3OQOCEKa29hjjQcII7p3R3RYRTN4EAykhkk+565VKyZAkZTwJosKsZuFPj5zL355xNG1NCV+/9Ba+84vHeWETOBXwm8B3Q5ZBCjiPpx9HL44UPzADRSSyUxLd7W1I40yI9dkQVEFcmMJVtmyuxO2Nyf8NbYZu6zMqhjnAnVcSlzIzcbz3wClMmng4513/W35200P0r1nDh48/gN0nlSmrYl2Yp8cBzpq8uD6UGUlslhHZiYkiuZ3xKC5z9VZp6gdPJ7OrEHrxKupTjHV0WM/bFkxgUsdBXHy151d3PsCrq9dz1imHsWTuBFqtUsajBryWUAGLQ6jlJ6C8g48oEhmZKJLbGWuCxaS7eEhOvQdNMdag3pHYlDbfxeKJTXS+781Mm9LGD69/hGcvvIcPvutgTjigk6mljJKvYXwVlQTB4IxBYg48shMTv5vbEQGSkgRhER1YuAsi4rGkOIXUNpFSRVRppptZTcpZx+3HRz7wdlQqfO+K27noxl/zbE9KaizG10iyFDz0SJk+KW3/Rh+RyBYSRXI7Y0QxxpCY0PRhZ0zcbAmCYsTjjaHPlOg1VVLTghWhTfqZVVbOPHQmn33fYma0KT/4+e187efL+M3ajP6kis8ycBnqFR8TN5GdmOhu7yB23nnCt5Q8iWMsHsgICZ2yVhDtoeq6mSZlTtmnjVkdR/GVa5fx0zueYvkGwyfeeSAHT26m6mpUXC/GlJAYk4zspERLMvIGkVAehKGCUgVKCJgySDOCxWiKzTay/4w2PnfWcbznyIN48JGn+PeLfsnPHnuFdaaMkRJWd/UbRmQsE0VyB7Ir524Ug5MKxkPVeVqco+xCByA1FZxpITMt9JlmPMr8ZuX/OXERn3nPwXR1vcr//PhqLr3jd6zsTVBT2tGHE4lsluhub2tUCDMMekRMmM9aLepNvRnvLul5i6AIpjg2BfLaSi8SfjD0G0sVT8U7ZjdZzjpibzo7ylzw87s4/8pbWbUy5U9PWMTu7UmY5lsVI1k+B5Ctnz/F5e9ZNPAtajaLxr7hZIpYdtlsWGSnJIrkNkTq/yvg8lIXQdSiajAiiO6al3QoLs9jqzYZZBYXU0MoYIxg1eYzODjGGcuJ+y6gs3U85//sXq645X7WbNzAWe/Yl31mj6cJBa+IIS89B1BEFS+az5pj6+cszNsYZnDM351d84xGdlaiu709aBi1EqzGnXOkzetl4CYgA+2NGo7VACKKGg8mdDEXMsqasf/cSXz8rLfztsPncfsDv+VLF9/IHY+/zCYMjjLqEyAF6cZoCoQbikExGqbCNYNuMLKLmuSRnZ0oktsZsYAJFlbwD3f0Hm1blBSoAS7omIKkNapZxtwJZT787jfzvlMO46V1G/jShb/i0jufYA1KZkPlpPEWRVFJQ22mKhbF5kIpPg9fYFGSWG8Z2epEd3s7MjBCOW+VNuYv6dDcI0w+azHeIGqoiGB9hhGludXwp8ftx9QJ47jwqmV864p7ebVrE2cds4hZ1RJlTfDicOIpqRTTUEJ+7lSC468aHG8brcnIViaK5HYmdNiR3DOVP4I5YCRYeGpRb3M3WSgbRyIpXms0GcO7l8xh4rgWLrx2GT+89iFWrq1x9jv2Y9GUZioqWFW8F1DNhXDA2Yd84jHhj+B8RrY3USS3N3VzUsZIZHJ0hIQQT8yPVfPGw0juNoP3Spv2c9yeHew2/gj+96pfc81dz/DUmj4+/u7FvHX2OFrSlMzmXTi9r99sQijyj+FMRnYUMSYZ2YbkwYVcIOlnPioAACAASURBVLWezSmeS8CXcd5REqUly9hvQpXPfOAw3nfigfz+2dV8+fu3cv39z7MeQ68RUmPIbCgDCrluD7j8MRLZ+kSRjGxTrHqMZGAcaj0u/1GrIZ4oFmssoXFaFUjYrdXy8bct4G9P3p9S7wa+dtntnHfr71ndUyMTyBC8yWcYkyCSoQN6xq5doh/ZGYnu9jaliJAN3IusOlDFExI3RmWrBtF2NolQ0Tx9k/8TRcTgAcnn5xZvEYGaNXiFcqbsUVY+dNQcZneW+frPf8d5Vz/Cq69u4Mzj9mPPiU2IU/DgrEVFMQ1JMEdjkswXO4LKQAw4uudbD23o+7fr9yQYThTJbURoSpsBgiNBxWMRylkf+D4yEhxK4n2YOnEr4HNByNv55omhIAtFcXcx77cwIKiDnmv4vfFRhzTAVAkdzEcjiGOyWeFWASfFhaWUceGWIuARxJY4fL/ZjBs/jq8vfZBL7nyBVRs28Tcn788+08aROXAmjOwp+TANrreeLC82T1Csd6GzsVpUEjITiuDt2LuWdxjOhSbSxhi891hrMVvpO70zEEVym6L1/7UQKvVkmpGGgSVghK3V38GoBx0YpTJc/goGZ4Y39/ugx6EiqSH1MppJtqVWbSYOj8cAVjxeBYchIwE1zJvZyqfPfjPTbnqYm29/kH/csIEzTjqEIxZNZ7ymlDNQ43AmLzVCAZuLe5EgC/+bmP7eqnjv6+IoIvWfsUQUye2MJ1y4zucTZRnZaimHYiJYRnwc4I3kgocJnmypCL52wbxVMGrqIqaA9Z6qDSO1rcJ+4yvMOHZfZrd38P1fPsp/XrqMFWsW8f4ls5hWzlCXolIhFAP5IJBi8MYiWEQF0ZBNL6zpyB+OqtatyKHexlghiuQ2ZbjZYhDEJHgkWJKai5v8oV8wwUtSH+08sHSwmA0MjXx9+JEkcZQNDX5m9GMzSn2YIT5UVooqqGAwlC1Iv2dmpcIHjtqLcZ2dnH/lr/n+j5axYWUXZ75jIbuPryKZwZosF/Bgm3oJam6EMJwRTxzfvfUorMYVK1awatUqFixYQJKMLVnZ4UczUtDXD2lVXSwfasYPvXNtiZmvqq+53kh3xJHeW0Q2e/ccWH/w814ENSZ0tMlfL+KGubMDb5Q/vlaIR8mH5uXuZf72vpglYqBMMY9TDtvjgTerBytD8fZQkS2Wb25Xw77owPqhOBLIj7dh/5QQl4RcyPIi+0LLvAYFdeIxAhOscNriTia3Hcq5S+/kolt/w4t9Kecc/yb2ntxMCwmJd8HZ1tA5yOVF+wYNcWJJ8n1pOK7X+d0pPvehf4+0rS21sLbke7m57+Fov78WQ4/l9WKt5bHHHuOzn/0sxx13HO9973tZsGABLS0twMD13Lj9Xckl36Eiqao45+onrIht9Pf3Y22Y69kYU49zNH7ZRhLILflyFu5B8ZqRvuxbIpLFa4uf4R+61oVEVVETSl68KplXUi9kHjKUkimUTBuURgbv6+ZsswYttpoGq0waRSiMcR4IT2rjqxuPqL5cNYigGAvehfhjkRkuGlmoMnSaxwGRbDyHPuy9zVvDqQ5oZj4pWgq4POPtJe8uZEBEERSPQ0oZXj1lLVHycNS8hI5zDuGiGx/n1rsfY+Wq5Zz9ziUcOm867ZrQSg2jLsR8TYKXwq7Pj7+4H7xBMSk+/8Yb+kiC2bh86HZGem40Rlp36Hs17k/jd3Ok145kjBhjcG7AH2k85iLuOPT9i+v4+eef54tf/CJXXHEFxx13HKeeeioHHXQQ1Wq1vm5xPb/eY9+R7FCRLD684sQ553j22Wd55plnOOigg+jo6BjxhG7uzjf0Qx9pnca/R/rQN/fBFRfFUDEt9n8o6n1+kTd8KQBrDMYmIR6J4K3gcrFRzQ0oGezJep/7i43bL/aLgdeUyPJ6wdDjcWBUz9C0zFCRbFwnHyyp+U4YWxfousA0FNgM3UquqA07mPd3FAHRvLB8sHlbJrc8tWHeRO/B5PFJBPEmP6QUVGjRhMUT2xl/wv7s0Vbh0uvu5n9/cAcbTngzJy6ZTROQaBo2haGWQeZSKloD8eGmpUqWZWRZNsxFdM4N+n4Ugui9H/FGWmxr0PnIhaXI/g5df+h7NL63cw5r7aDl3d3ddHd3D7omrLX09fXR3d1Nf38/AEmSYK2lVqvR09NTX17gvae3t5darVZfVsQUe3t76enpoVarYYyp//T397Np06ZBAioiZFlGV1cXq1atoqenBxHhiSee4Omnn2bp0qUcddRRfOQjH2HJkiWUSqURDZOdnR3ubhdfpGeffZZrr72Wiy++mIkTJ3LBBRdgra1nz4a+Zmsw9Ev4Wtt/Pe6CWAuUAJOf5MKnLOHUgISoWV8mpKJ4Be9cEERVvIaeiqiSZp5MB98AvCpp5gZimaqoByuCc57M+Tz+6Ouy6D04nwtoA+oG3P0Bq0NwXqilHud0kLvuXRCEQe9PLhRpRi3NcOowIniT4BXSXIy8V6Rhn533+P4a6kK5lJEExJB5T5alpLUaqj53xQUvntQ5ar0elwm+BOtNgrXt/PbZGv972V08/utlVFf+jmr/BkSULl+mJwV1NRJfw6kDTDhPWUaapsMErqenh76+vmE35/7+fvr7+wfmTc8f0zSlVquRZdkgEUjTlJ6enmEWZ5Zl9PX1kWVZ/e+CNE1HvOGPRqOx0UjhkQ2l0UNrfN4YM6yEp3jeWjtM7Iv1s/rnG67XLMt44YUXePTRR3n00UfZd999KZfL9ed3FYGEHSSShQXmvef555/nxhtv5Ac/+AF33XUXtVqNI444ghdffLH+ZSzWTdO07p4XH2Lhnhf1WY3vUavVhn3ZVJU0TUnTYGU0fkmyLKNWq41ooQ69Gxdf7DRNB7tsClmWUktTsrQH55SMMsGeMTy4PqMVzx033kLy1B10tE9mkzRTy8IFmGYp3vncwgAQ+vr76c1qg2KJXj19vX11iyNTpU8t2DJ9/f309ddy4Qxdu1Uhyxy1tIavWwP5Ptdq4AdSM6oG1ITssAvLxdo8CZKv5V1uAUvdOJW8/VuaZuF9RcCU62GGPBeTN/jI7VLvyXw/XjyQIDYBSRCxZC7F+RTUhea9iUU0TPWgLsXicb5Ev1aR1vGUK1VWrlvHxRfeSvrU7TRlXaDQb0uYcjPGGsTVKCxZEaFSqVAul4eJZKlUolQaPK1EYVUlSTLMszDG0N7ePqJnUi6Xh93orbX1n8bvZrF+qVQaJkjVapWmpqZB66sq5XKZSqVCqVQadF0kSVJfPlQIy+Uy5XJ50P4Xy6vV6iAR9d5TKpVoamoaZHGrKkmS0NbWxsMPP8znPvc5XnrpJZqampgzZw7HH38855xzDgsXLqzv165YPym6HfP2jTGc9evXc91113Huuefy0EMPsWnTJmDgyzZnzpxBX8biTjXS9goXYOihFKJa0CiGI4ln4f40vqZ4Lk3TwReABgssc9mAh6nBFTU2dB031jTE7cL0Db55Ir55OkmpwpRpkxg3exEbkslkaoBgQRYYEYyEgpbM+MEJl7rXqhgT6hV97tqH86KIMdjEhkYQ+XEYzQvM8/hQcaE26l/dmR5kVSjqG9wk0SBc1mDE1BM8YgyNvY1KNsmHHTZYZFC/ARgriMkQm+brmCCquRuaJKGtXAlP4jPEh2M1EmpCBYtJyjhVTNbPrCbh0PlT6WzyJGk/1hjElpCkku9bYWGTbz8Z0UJKkoQkSYbFD4eKZEFxHkfyeoaKVBGbS5Jk0PqFSA58Jq8dChotpro9rbV77rmHM844A2stp512GqeffjoLFy4cFI9sjOVGS3IzNNZUiQjr16/nxRdfrAtkYzKku7t7ULyoWq1SqVTqX8TiDmytpVqtUi6XB92VRYTW1lbK5fKgZcVdt1i/uIN676lUKjQ1NQ2zIJIkoaOjY/Aym1CtlKmUKyTFRaCgolhjSaxFSjbEBdUjeGxS4sab7+Tz//SvvO/jn+aEPzmT9anQXy6jMrDvRiQXIEtihMRCSQb3nlSBklWSZCClY7TBlSV8Ia0xdX0SyKeLCIJmBKwYsGZQEFRyi8/mrxcZPEKHPBkkIiQ2jLsJ0yswbPRQRUx4j/orG7cjGBveZ+g1o6ogYWRMMTrGy/B4qjUD00WIV5oEWqoVms0fR2egHS02Rby1paWFT3ziExxxxBEsWrSIpqamegy3uMYKdvQ+v162q0gWJ9Q5R3t7O3/+53/O2972Ni677DKuvfZaHn74Yfr6+thzzz357ne/y9y5c+vubHGiN5c4GSmDt7kPoxDToRnKYvlI2cmh8Uv1Giw0M/oHHipZ8omqsCxf/ipoL29aMJ3jj9qLLIOyHdJ8V/O/hbygR0lk8EVfZGobl5mQJhoy3HBobEsHWaQGM0JJ0MB2tS5rg1u7KQreDRjKmu/3iO7UUAVsXJxnq4YOOzK5aet9eBAwSYLWrVQdtKGQwDLUXPhsaupDK7b6eTPBhiwEdde6TndaRIRarcbcuXNZsGABpVKpLo7AsGtrV2S7imTh1hQZwiRJmD9/Pp/5zGd4z3vew9KlS7nyyitpbW2lpaWFlpYWsiyrux4jlQAVWfHNZZlHK5so4i2N2y8Eeej6I5VLKIDLlzcaObnv6ou4m/hwiYpFNA8ZpDXKHipA1Q+xEgeJdC5TppAyrb8F9brD/HdRvDYK2cD/jVsLbnH42+VutAxZZ1A74OCbDhFyQtyyOHwxoZnFSNXsQ1zNugjXe0w6hr0w71IhRgbkWdMRS6EG4sGKweLUhydMCCtgDI2HE9l6NF4/xfUEwSAqPL5dfSTOdne3izhQIWxF4HnRokXstddenH766Tz//PO0tbXVY5BDM2KFyBbb3FwweHM1XcX6xT40CvBrfajF67339Yt4pHo0ReozDdQFocFlLomnSi5SDdYfAA2uYpHscPVDzG1IVVQFYwZPAmEYbKjpEFnxDJbNIp466FSpUAyWbHSNh2mMGSzIAuiQj0LJ3fCBzTQ+5KWbpXy89bDV6r+Fm83gZ4YSjkOxubVocpdd889K1eRF5SO9NiroG2FoHXNjPWVxLe2KyZpGtrslWX/jEYYuFZbl/PnzR62leqMnfahLPjSGORojWZl1cc1jd4PEVYrLufE9B9TIoFijGHE4GWp+DRYyQSjrYHnQYnPDPOVBJu2Q38OjNiRp6s8M2o4fvMLgNRv+GhxrHOkMBi98qDXbKJKCqEG8GWr0DsIbyGxhVw96dUO4IAh5YmxI6miebDIG9aGJRoj9KviB8cYjhWoiW8ZI1+JYO687vE5yc+xMJ7exeDjLMlatWpVHxLQ+fK5aqTBh/IRBMblg+DTG0Bo3WqzjsfpaNXFmmJBt/uzoKL8XtuVreJ551nw00Qpi7+su83CbstjPIpk0PKIafs3fR/yogUKLw3jHUIltPLeCxVPKBxXlXWmMgCnn2xggzSschoZxIluHnen6/UPZaUVyZ6OIvaxdu5bPfe5zPPf884jJ69GM5Zi3v51PfvKTdLS14+oxtzBHNIDmQudz68sXrqMmiI7+MRTu9tZoqVaXtFEFcCADLg3Lhq6jIy0fwmvqjwBSdBYvFgy9sQR70RSCupkbgRaCrAOxyMd/+1uWPXA/TiEFVIVJEyZy9NFHM66jY8QRL5FII1Ekt5AiMdTV1cWyZct450kn8fZjjyXLUlRh2vRplKvVPMZIQ+xrcNcZrdsz+VBEkby0ZfMUkvHal7I2/MDI7jYDk3JtdjOFZTbASLbb1pMWec0bBQiZyOhvqop4wRTDH71yy0038i//8UUmdE5EjSVzjnlz57Fon30YP25cPYa2q40CiWw/okiOSKMsKabo4ZU3kCgnVfbb70COe/vb66/w5GOsNc9n1E2ootwo/DXsMpTGmNrICHmLtdfc5+HlPsN/H8H1H3VbgyWxHtncYpXcAldWhcHO8Oa3Mpq+hzOZj1TKG1N2bdjEHjP34Dvnn0fnlEnUfI1yUmZce8egqogokJHNEUVyGAPjlBv9SREXRqAYg9UkjDFuwGUOERMyrMhmA9f1Yu8G0bRboDZbtoZli0RJXsvd3gK7dUs1ZStpj8hryWhYKbMGLz53zQ2JrQAJUzun0za+DbUeKwZ1DW56jElGRiGK5JYghYsarvhalnHnnXdibGg8Ua02cdghhzB16hSKxMjruey2rg2zhVt7zdW2o2W1lXZ5pHOugDUWaxPK5QSHw7sBi3ukBiqRSCNRJLcIybPWISaWpjWuueYa7rjzNtIsZfacOewxezbTp0157URFZPuiyosvvsCf/Z8/wzYZ+rJe9nvTfnzmU5+mvb19lxtHHNn+RJHcEjSfDEBCLV+1UuUvPvkJPnDW+6jVaiRJifbWVlxexRIvuZ0Hayylcpl58+ZRaauSST9zZs8GBtzs6G5HRiOK5DCKmsjGuF1eFamhy3ZiLePGjWfyxAn0po4ksYiPF9rOgjbUnaZZxtQp0/jc5/6e8VPa8plvTH34XGFJbkk3+sgfJ1Ekt4AwqMaAd3gXphEw+ZC8JLGhS42R6GrvDCj1jkx4j6hSS/vJXA3vlZQUK0m9M1EUwshrEUVyCwjXkUeMwViLyxzf+c53uPm2m/DqwXsOPOAAzj77bMZ1tO3o3f2jpbFCVPMqBbF5HyUXmv6aKIqR10kUyS0kDOLwNDc3ceaZZ/LcKy8hSd5AwSnlcilaJTuYYYVLxtLU3MqMGTNzlzoU78dcduT1MEZFssHvVRnoyOUd4PAqGJOE4m8EGVSAlxeQD9rWQLHzxM5J/O3ff3rE7IxXJXMOQ5ivxtpkoFNO1M8/iOA9K/gUYwTvPCYp5/OXO9RneQikhHgPPkWt4Z3vOZU3H3kUHeOaMGQoBtXQVi58JI0F+AMyqxqK951L805r4TugqhhrUHUIPrSZMxZVIXOeJAld2Bvvl/Gj37UZeyLZ2HMyb9IQ3LBiTpUaSoLPLN4rxoCxUEx9CqFLt6+PAw6NE0RMqJUUwmTWonijdetENUwqlSA4r4gPk3vZUnnwoJV4xbwhnPM477GqoSenU5wINQxePVbDRGLqBSQDl9HvEzpnz2LG7FmY/g35fD9NiM2bc+QjiwbGDoQPSBHUQeocmHxKD68YKaMIRj2KQ10Nq2BKFdIsDLXy+SCD0AE+32r0MHZpxqDnIYN/Ggy5MFWrITEJeEVUwyx8CkYFo5K3HpMw/k0bVS1XOsl/Btr41H8v+lxaY/IpCcxwUYzJnTdEkYyRYgoHI1x9zc+59trrAKnHGq0xYS6bJCEplahlSubDNLs3/OI6LjjvArq7expik7koDvmuIEUs2mBMQqXSRLlSolxJ8gFLirGWdevWcfmll/HE448jYl/3LIeRnZ+xZ0k2itKgEYChy0yWKr3dG2hubQuy50BM7m+LRxC8Dh0Al49lltz6qA9XHHyPMXkH7I1dGymbhEpLa33VaEv8YYjk0+d4D4nh5edf4LKfXMZb3n4c1iZkff0sX/4Sjz76JCteeJrOiR3sf8gRTN19PoggYrn5xpt46IkXOPW9pwFNFAJZf49BQ90d3jswhvXrNnLvsvt49tln6Rg3jgMOPJC5c/fAWktzczMPPPgAv/v9U3xm/p5Umirb+cxEtjVjTCTzesaiww4UTnY+ZjrhisuX0rVpI2effRbVShWDyadCHRA9Q/CoR8bnccZS0eURACchPpU6x5U/vZJxbe28892nIA1jvBvt0mhQvj7qvoEoPsu4//772bipm0MPP5ySCC+sXMl3vn0u69ZtYuOq5ax86Tlap17BZz7/Lxx58AGERiVgxNS/EzDQPb7+HhrsSu9TjBVWrHiVr3zlq/z64V/T3t7Cpu4uLr30R/zlX3+ao488kpb2dhYvXswlP7qU9evXM6V56g46Q5FtxRgRyaIA3OPzKViDy6yIOgwOMcLyl15m6dLrOPqYwylXE8Q4Nm3s5eabbuOWm26iq3st++2/L8e981R2mzUba/NtiKLqMOIRUVavWsn119/EnXffR+ZS3nzYYZx4wolM7JyITRLK5TLnn3ce+yzen90X7InmDdLsoAL1QNFILTI66hU0TMNQ6+/jhptvZNqM6UyfMQMVaG/v4OR3nsTue8yjc1yVe26/g499+h+54vKrOWi/fWnLp91FXL3JiOaNPJzmk7oVZUMoYjxiLEuXLuX22+7m81/4B956zOG88OJz/N3f/yMXXnAJB+6/mAkT2pg/bz7dPT089eTTTJs+Nd4Axxhj5vqUeiB+wH4s+libPFB/x513smr1Bo446i1glP6sl0t+eAn//h9fpFbztLd38NOf/oR//Id/YPnyV3KBJA/cO2ppyoYNG/nPL36Z886/AGsN5XKFb33rm/zPV/+H7u5urE04+OAldHV1cc+yZWQojoE5eUbq1Rgvqi1Bc5dbWbtuDY88+jCz58ymvaUZD0wcP4EjDzuCadOmUq2UOejgJSxYsCcrVqzMEzZhnnBVx+9//3vOPfdc/vkL/8IvbriJnv6UELXMy4Q0tMer9fdwyy23cvAhb+bYY99BS0srC/fah1PffQpPPPEky19ZBcD0GdOZNnUad99zz7BmdZFdnzEjkgGtd0L00DBBkSfr3cj9y+5j9rz5TJ+zG0aEhx59iEsu/QEf+vMP89VvfJX//upX+Id/+juW3X8Pt9xyc5ipL5//GhWsLXP7Hfdw/S9+xaf/5lN88xvf5Bvf+Dof+/jH+dUNv+KRRx4BlJmzdmPylCnct+xeutJeUudD0TkQh+W8MUTCvECosnz5crp7+pmzx+7h886NTMjnVkkS1qxezZo1a5k8aQqJLcIvytPPPM2///u/ct2113HbrbfxN3/zKX669GpSXzRLDj0pjVHWr1/N8hUrmDF9JuVKgvcpkDF58iTSWsbq1esBmDBxIjNnzOSuu+4iy4bPVxTZtRlTItloo9UvnnxpV9d6nnz8CWbM2p2m5mYyPL99/Lf09vdx6JGHoQJprcY+ixYyZ84sfvu7R6jV+vIZ+ARrErwT7r/3AdrbxrFkycE4lyEIS5YcTLVa5bHHH8Orp1qpsHjxYp574QVeXbMKNQPRSJExdcq3G0LeGFeV1atWUa6UmLXbbsFyq2e9BWMNrr+Xq668Eu89p77nJGySgIdSktDT08O7T3k35194PldedRWHHHY4P7/2ejb19AOhFlPzEq/e3m6cczRVmwlv44GUSrmMqpDWUiDM/tna1srq1auo1dKYpBtjjLErdiAtYvIf9RmCZ82rr9Ld18P4aZ2IETwp619dxYTx42lpH4eTYH22NDcxb/eZrFi5gv40JXMZ3odauVp/DytXvsKEydMoN7eSuRRBGd/eSlOlwvKVq0h9EOYDFr+J1a+uYs2q9VixRT0JOmx6w8iWEUIeimfd+nVkWUa5UgnWnwb7T4yi3nPLLXfy48uWcvr738+SxYvzggRLf82xaO+9OeWUU2hra6O9rYW9Fy5k+cuvkPal9SpJVMAbjFhEPWnaD5oXs2Nzt1xDwk89NkmoNjWBEVyWDuxyUS0W2aUZIyIpKBbBYFRIAOsd1tfyImPPhnXr6Cejbfp4FKXiHbqxlwoJYhIyAcRA6miTjMwpNSnhvMdrhhNPmnbR27MO0zGOrFQOV4D2UTYeRejJDP2SoKJMndhCz+p19K2tUWrMa5vC7c7/VKLlsQV4FB/qtahUm0ES0poLp1EzRPqBPm65+TY++am/520nvIsPfvBsqlYR73CSkJkqSamKMeW8prWXsnfYfkhqHusdQoa1JXxWprV5HE0VQ3fvqryzUBlPE719ICVoG9cEeLwPQpplLpQbMVBM3lBGG9lFGSMimaN5ZxdClY41hKFqqtRqNdLUIcYGOXVCxZbIanlqJU+Il4zBe6VUrqJ5x2pVxSQJ5VKZcmLp7e0Oww+NBedxmUM9lCuV4P4ZQ6mckNh8lI4yUC4UY5JviEJsVIXOzkl4p6xetToMgPKKesfdd97O//z3VzjhxJP57N/9HePa26iWbbAOjQWTkGUe5zzqPUYcpcSSmDCDkKCk/X10bezGZdDeNo5p06bx5O8fZ+3aNZSShP5axkMPPsjkSZOYPLUTgP7+ftav30hHezvlcrm+v/HmNzYYMyI57EspYYyu92HoRLnahDGWrC/EnkiaGT9pKuvWraVr43oSAwZPb28fz720gskzZmJsgrUGTxgSVyqXmDp5IhtWr6LW24s1CSRVNnRtolbrZ7fp0ygbQGHDxk2oCDYJ8978/+2daZAU5RnHf+/bPdfOzB6zyALLgiIshMMIRYxZDpUUwQVkoxEwlica4oUpquJV+ZCKSVUkH/IZrJTlhxhNTGKsIikDaIIYFVxNVcAol7CKyLJSmAT26u73zYfu6dlB3RjN4mTq+VVNzdHdU7Pb0/95nud9DhOPlhU+DUoptOuilKJpdBPWGN7pehsNJBMJDh8+zI9/tAHP91jytcX8bfdudrzwF1588SX6+noBG42PtSilcZxQGK31CYIAayxaO+zqfIX7H/ge+w4cJJGp4fL2y3ml8xU2btrEyy/v5OGHH+bJX/2apcvaGdsUjus4depfHD/ezdRpU3FdV85xlVEleZIRKoonRXVlphjsx6G+0IhCcfJYT/jLoBzGt0wgCDx2vfwi06ZORmtN56t/Ze9bb7Ps5hmkkw6+18f7x7tJ5UfRmE0yffo0nnh6K/veeJ0JC+cTBD47d73KwIBH6+TzSUQf5cjRbvL1tdTVZwlMadjXf5p5KHw0gVUYG2YajBnTxHkTJ3LwwAEGBj3SCZd3jxxl/4GDGCfDPffei+97OK4mk0nz6KOP0NraSmNjgYaGeqwN295ZG1BTk+GccwokEwoIOHDwANuefZabbrwJpR1WfP1K+gd9Hnv8l/z8sV8wYeK53H7HbVz1jatCC1U59PT08M6RI9y8ZBmOUzV2hxBRRSI5tJtgJEi2VHbW0NhEaalNeQAABxJJREFUobaOk0ePYgKL0Zo5F11M2/wFPPKzTfzjgxMklWXbM7/ny23zuGThAlwFPUePsHLVtVyz5nbuXns9l1x6KbOe3sJPf/IQe3e309vXz29++xRLly3nwhlfwLE+vjfA7r/vpWHUaOob8qUgv/CpCVO5FL7nk8vVMX/ePLb++QW6j3Uzcfw45sz9Ei917sQ3CfyA0AMwAVpr6urCWTZ33nkbFk0+W4s1AwQ2YPXqq7n6qmvI5XL09Z1i3969XHzRV5g0aQoYQz5fyy233srK1d/E8zy041KTzUaTMwEMh7u68D2fObMvrB7XTIipIpEkyiOPrEkAR6OMQxB45OsamDlrJnv2vcE/P/iAdKGW2roG7rnnuzz1u6fZ8fzzOI7DkqVXsOLKK6kfPRplDadOnuTYseMkMxkC5TKmuYWHNjzE4088yZYtW0nnall7x10sa7+cXCaJMh79vafZ/cZ+Jp4/mUKhgOOErdNwwpZaZYh2fjKi+uswKdyyYN58nnl2O3v27OHclvGk0jVkMxnQqTiTICQcu2Gx5GvzKBysCT0MrRwS+RQEaQyW1/fs5sSJE9y1bj2FQh6UQUeWYX19HXGRa7hahCJgoK+P1157jVmzZtHc3CwVVFVIlYhk0Yo0qDDlGKOiBGMLoEmk08ydO5ct23Zw+NAhGuq+iKMVLS3jWfutW7jxhusBl0wmg5tO0WcseP3s+NNWpk05j0sXfZV+A1kcWltbue++e+nr9wiUSzqXJWEV1juNSmkOHzrEsZ4TrLppDdlMGkOAo8Td/kxYsEqj0VjjMX3GdBa0tbF/735OL1xIXU0SG/hh9oDVpYPiGpjwy2DLotdhXZaxhgDD2HFNrF+/ninnXxBW3sQhkmjXOBO32DlF0d3Tw/vvn2D5sqXkclmCoCSsQnVQJSL50dio35WjXQIT0NZ2MZMnjWfbH//ABbNmoJTGWp9MOk06VYO1YdDd9z1cN8HRrkO8985b/OCH36e5ZSxYi7Uug55POpkklcwygGLAt+FKqaMwgwPs3LWLprHNXDh7TvFTxDNxZF7YZyRyu2vSab5z9zpODxrSqSTGAMbgFPt2xthSP8/i8zPQWmEsNI8NywsxOo5rf9xSm8IS+D6NhQIPPHA/+doG/CCIRg8L1UQVieSHky7Cvn8uxvpoYHRTEzdcdy3vvtfNgDeAm6pBBRoTBHGisI0qbKwxnDN6FN9et45R4yfTG7+pi3YgCCxWBfjWxdEKh7BbttffRyaVZs2aNUxobsYSoOK6H6fcExQ+MWHLubDHp9YOJgjIZXOks6ELrrBo7VIStVId/5mx6pBojjoKVNgk2feDqKpHlTQyOnulI8urs5OpFKPSWQI0vu+TSCX/13+68DlTHSIZN8ctts1XOLb0sjUOWmmssSxZekVYoaHC9WYVdd11bXjRhOWMCgdI5RvJ5+owSpO2FkU49kGp8BhrFZnoXluFSqZxE0muu3ENRoWVGeE7DulqXlRJEcv/Ch01wVVWY4nik0rjRELooEC50U7Ff+4Qt3poT08V7UsmShUD7TigUih0lI85NLQ5NEhSshS146KsE261FieVDPsF2LAuwdroSDnX/9dUh0jG18SQGNLQ72bRBVJlu0VPnPJtgEOx6a4GXDRQaqVa2r/sWlSasgsoflb+/sKnI/YTVNH6C18vH0+kzzii9Lg8hxbCs5OMDwu3J+PtH3+6SluUKnkGHxqTBOI1VAkSQBEEQRgGEUlBEIRhEJEUBEEYBhFJQRCEYRCRFARBGAYRSUEQhGEQkRQEQRiG6siTrGCMCTtXa63RWsdTE4c+VkqFPQ2tjfcTBKEyEJEcQYwxBEFQJojF+6J4Dn1NKRWNFbDhhEZBED53xGQZQay18U0Vq4Gie8/z8DyPwcHB2IIMAhlHKgiVhojkCPJR4li0ELXWpNNpEokE1trY4hy6ryAInz/ibo8gYTdtS29vL5s3b6arq4s333wTgO3btzM4OEhtbS3t7e20tLQAJetTEITKQFm5IkeMYswxCAIefPBBNmzYgOd5uK4bL9SsWrWKjRs3ks/ncRwnGlalZPFGECoEuRLPAlpr1q5dy+zZs4GSO10oFOjo6KChoSF2w+U3SxAqCxHJEaboPre0tLBixQpSqVQshG1tbSxatAgIhbNoQUpMUhAqBxHJEaYofgAdHR3MnDmTIAjI5XKsXLmSMWPGlK2Ci0gKQmUhIjmCKKXwfT9ewJk6dSodHR1Ya7nssstYvHhxWa7k0JsgCJWBrG6PIEopEolEbBkmEgmWL1/Oc889x+rVq2lqahLrURAqHFndPsv09vbS2dnJpEmTGDduHMYYXFd+qwShUhGRPItYa/F9Py5TPDPBXBCEykNikmeR4up1MReyeC8IQuUift5Z5swuP5I0LgiVzb8BhTwF7hiYJsUAAAAASUVORK5CYII=)
Find the midpoint and length of each side using the placement
below. What is the advantage of using 2h instead of h for the leg lengths?
![](data:image/png;base64,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)
Maths-General
Maths-
A sum of Rs. 4,000 is lent for 5 years at the rate of 15% per annum. Find the simple interest.?
A sum of Rs. 4,000 is lent for 5 years at the rate of 15% per annum. Find the simple interest.?
Maths-General
Maths-
Place a rectangle in a coordinate plane in a way that is
convenient for finding side lengths. Assign coordinates to each vertex.
Place a rectangle in a coordinate plane in a way that is
convenient for finding side lengths. Assign coordinates to each vertex.
Maths-General
Maths-
MN is the midsegment of △ ABC.
Find MN.
Also, find AC if CN = 35 cm
![](data:image/png;base64,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)
MN is the midsegment of △ ABC.
Find MN.
Also, find AC if CN = 35 cm
![](data:image/png;base64,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)
Maths-General
Maths-
In △ ABC, AM ≅ BM
BQ ≅ QC
Prove that MQ ∥ AC.
![](data:image/png;base64,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)
In △ ABC, AM ≅ BM
BQ ≅ QC
Prove that MQ ∥ AC.
![](data:image/png;base64,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)
Maths-General
Maths-
Write a coordinate proof.
Any right isosceles triangle can be subdivided into a pair of congruent right isosceles triangles.(Hint: Draw the segment from the right angle to the midpoint of the hypotenuse.)
Write a coordinate proof.
Any right isosceles triangle can be subdivided into a pair of congruent right isosceles triangles.(Hint: Draw the segment from the right angle to the midpoint of the hypotenuse.)
Maths-General
Maths-
NQ, MN and MQ are the midsegments of △ ABC. Find BM.
![](data:image/png;base64,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)
NQ, MN and MQ are the midsegments of △ ABC. Find BM.
![](data:image/png;base64,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)
Maths-General
Maths-
MN is the midsegment of △ ABC.
Find MN if BC = 35 m.
![](data:image/png;base64,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)
MN is the midsegment of △ ABC.
Find MN if BC = 35 m.
![](data:image/png;base64,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)
Maths-General