Mathematics
Grade9
Easy
Question
Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the last statement of proof?
- A
- B
- C
- D
The correct answer is: C
The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
Related Questions to study
Mathematics
Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the third statement of proof?
Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the third statement of proof?
MathematicsGrade9
Mathematics
Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the first statement of proof?
Arrange statements A–E
Write an indirect proof of the corollary:
If ABC is a right-angle triangle, BC is the hypotenuse, then ∠A is the right angle.
Given that ∆QPR is the right-angle triangle, QR is the hypotenuse.
A. That means say ∠R or ∠Q is a right angle.
B. But this contradicts, the given statement that QR is the hypotenuse.
C. The contradiction shows that the temporary assumption that ∠P is not the right angle is false. This proves that ∠P is the right angle.
D. Then, by known theorem, you can conclude that PQ or PR is the hypotenuse.
E. Temporarily assume that ∠P is not a right angle.
What is the first statement of proof?
MathematicsGrade9
Mathematics
Apply the Hinge theorem to the given figure.
![](data:image/png;base64,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)
Apply the Hinge theorem to the given figure.
![](data:image/png;base64,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)
MathematicsGrade9
Mathematics
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find AB, if BD = 9?
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find AB, if BD = 9?
MathematicsGrade9
Mathematics
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find the possible value of BD, if AC = 7
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find the possible value of BD, if AC = 7
MathematicsGrade9
Mathematics
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find the possible value of AC?
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASkAAACyCAYAAAAeTzm2AAALLElEQVR4nO3dvXLaWACG4U87eymQYidXIK4A0rhKm04qQ5MuZTo3ooRu21RuVroC6woyLiLdi7aQhTHhX0fo/LzPDLOEtTFI8utzBEhR0zSNAMBSf439AADgFCIFwGpECoDViBQAqxEpAFYjUgCsRqQAWI1Ioad67AcAzxEpGFJrNYsURbuXmWZpQcbQC5FCT5MT/69UuVlomhZ3ezTwD5GCYbGyqlHTNKqypL3p129GU7gZkcLwPn44Od4CTvl77AcA35RaTiMtu3/Gmar1fMwHBMcxksKwyqWmsxXTPdyMSMGwt31STVMpiyWVSz2y7xw3IlIArMY+KRi2t09KkpTogd1SuBEjKQwqTjLl1Vo0CreKOHwwAJsxkgJgNSIFwGpECoDViBQAqxEp3CyKorEfAgJApHCTKIrUNA2hwuCIFK7WBUoSocLgiBSushuoDqHCkIgULnYoUB1ChaEQKVzkVKA6hApDIFI465JAdQgVTCNSOOmaQHUIFUwiUjjqlkB1jIWqLpTuniprlqrgMJ9B4SgI+EMXFxObRr/7KpRGC232b44zVc9fOblDIBhJ4Z1u9GTqb1d3XzePquJE+f4pssoXVUYeHVxApLDVZ3p3zm2hmmv9vNZ8O2T61f4nedBcUr2atVPA7uSjRaooijRbMR/0CdM9SBo2UL1+TpEqWuxM+N5N9d6mg0le6Z8fUy3LRHnDkUB9wkgKdwuUZGCHernUl+1p2+da5+0UcLOYallKcfaNQHmGSAXunoHqXBWq+Xq7X6vKM8WSys1Cb5361p42S5IU6/Mndqf7hkgFbIxAdS4KVZFqlhbbE4tOpn9+Sb360o6g4lhSqSUn+PMOkQrUmIHqXBKqcrPQtHuP1HSpUtLbKbIKPS5LSYm+P39XIkmbH2K/uV+IVIBsCFTnZKjma1V5onjnpt1TZBVpu9O83Q8117eM0ZSPeHUvMDYFapetjwvjYyQVEJtDwOf9cAyRCoTNgeoQKhxCpALgQqA6hAr7iJTnXApUh1BhF5HymIuB6hAqdIiUp1wOVIdQQSJSXvIhUJ1TodoeCI+Qee3vsR8AzDF5sDqbHAuVb88ThxEpT/g0epL+PIV799x8e544j3eceyC0X9zQnm/o2CfluBB/YdmhHhYi5bAQA9UhVOEgUo4KOVAdQhUGIuUgAvWGUPmPSDmGQP2JUPmNSDmEQB1HqPxFpBxBoM4jVH4iUg4gUJcjVP4hUpYjUNcjVH4hUhYjULcjVP4gUpYiUP0RKj8QKQsRKHMIlfuIlGUIlHmEym1EyiIEajiEyl0cT8oCvh6szja7oWJZu4NIjYzR031x8Dz3MN0bEb8o4zE3/au1mr0da727zGapiro2cP8gUgZdc2IAAjW+IfdTleVGi+lUaTHI3QeFSBnUNM32cipYBMoe5kIVK6u69V8pT2JJ0maRik71Q6QGcixYBMo+5kdUE83X/yqLJWmjJyrVC5G6gy5WHV4Kt88Qofrwsb326zf7pvrg1b072R9B7f5CMLKyQxcq1oddiNQdHNrwDwWLX47xmQtVrd+/2msfP0x6P66QMd0b2CUb/P50EOPqP/WrVaRftCwlKdHD3NADCxQjqQExdXDX9SOqUstppOXerUm+Fo3qh5HUQAiU+24fUcWK40R51WhNoXrjNOsDIFB+4MUNOzDdM4xAue1YmFiv4yFSBrEhu+mSERNvTxgPkTKEDdgtt0zlCNU4iJQBbLju6PueNEJ1f0SqB96E6QbTO8A5eN59Eakb8dfUbkO/MsfB8+6HSN2ADdNOY7xlgOnf8IjUldgg7WLDe5kI1bCI1BXYEO1gQ5j2EarhEKkLsQGOy8Yw7SNUwyBSF2DDG49rr6IRKvOI1BlscPfnwqjpFEJlFpE6gQ3tflwP0z5CZQ6ROoINbHi+hWkfoTKDSB3AhjUc38O0j1D1R6T2sEGZF1qY9hGqfojUDjYkc0IP0z5CdTsi9YoNyAzX3jJwT4TqNkRKBKovRk2XI1TXCz5SbDC3IUy3OxYqtsXDgo4UG8V1CJM5h85EwzI9LMhIsd/kcoRpGATqcsFFitHTeYRpOMf+QLJdHhdUpNgQjiNMw+FsNP0EEyk2gMOY+g7n2mVLqA4L4gzGrPj3GDXZje31Pe9HUqzwFmFyByOq97yOVOgrmjC5i1C98TZSoa5gwuQPQtXyMlKhrVjC5C9C5WGkQlmhhCkcoYfKq0iFsCJ5y0CYQg6VN5HyeQUyaoIUbqi8iJSPK44w4ZAQQ+V8pHxaYYQJlwgtVE5HyocVRZhwi5BC5WykXF5BhAkmhBIqJyPl4oohTBhCCKFyKlIuvvzu4mOGW3aP8unjduZMpFz6a8GoCffWbWcu/Z5cyolIubDgCRNs4OP0z/pI2bzACRNs5FuorI6UjQuaMMEFPoXK2kjZtIAJE1zkS6isjJQNC5YwwQc+hMq6SI29QH1+KRdhcj1UVkVqrAXJqAm+czlU1kTq3guQMCE0robKikjda8ERJoTOxVCNHqmhFxhhAt5zLVSjRmqoBUWYgNNcCtVokTK9gAgTcB1XQjVKpEwuGN4yANzOhVDdPVImFgijJsAc20N110j1WRCECRiOzaG6S6RunZIRJuB+bD143uCRurbOhAkYj40Hzxs0Upc+UcIE2MWm6d9gkTr3BAkTYDdbQjVIpE49MRvnvAAOsyFUxiN16AkxagLcNXao/jr3BfVqpiiKFEWR0uL01+4+ke57utu6CwD37L7yd29nIlXocVlu/7V5Ol6p7gkQJsBPY4XqdKSKJ20kxVmuLJa0edKhTO3uZyJMgL/O/m7XhdLZ2+wrmqVa1f1/6FF5okaKm6zqrqtJ8vdfI4kLFy4BXU4E48j3JE1+/LvOOrHjvNDTRlL8WZ8m0uQhkTYbbZ4Krefz7VcxagIgFUoXm/ZqkqtazzWRVBcrPf546XXPUXOsMkWqaLFRnFV6/jppH0S00EaxsupZXye9fi4An7z2QkqUN2vNz37D5Y7ukyqe2iqWy+nr/HKh11v087++k0wAPql//2qvJA9GAyUdjdTrVO+I8ud/IlMA7uFwpF5f1VOSv3vFrmlyJZJU/hSDKQCdyYeP7ZUj7wDo42Ckuqle8rA/cJvroa0UUz4Ab+YP7QBGGy3S4m2mVRdKZ2mvcB3fcQ4AV6hXM0133vz9pt/O9LMfiwGAS0y+PqvKE8Xxzo1xoiz/1mtnOiMpAFZjJAXAakQKgNWIFACrESkAViNSnqiLldLZ24EGZ+lqoE8F1Frt/Jzt5dwREYEbjXKadRhWpJou3n+Oqdy8qFpLfA4crmMk5bxaqx9toOKs2n6Eqar6vTflvET57kem1sP+NISLSLmu/k8/S0lxpn93jp8zmbTXt8eo76ZjRdpOB3sfLnGjxc7RFws+JYWBECnXVS9qP4jwosd3+6TaKE2+fm8/U7VZKC26UVei7yYPCFZutJj2+3wWcFSPo3rCBkcP2bpzqOe9r4mz6uBdVVl80de9+548a2Kp6Q4zDZjGSMoXcaaq2x+VtR+e2p7dZ/5N2fbzVLE+fzI3iprMP+lzLEmlXipjdwtsESnXTf9R24gXVbUk1apeDykd/zOVJNWrL1qWUhzHkkotHw9PzCZfn98dP+z50JSwXindORRHXTyq/eB7rNcfB5g17kAO/VVNFh+a7nXTr7xJtmfs6K73mJpV3fRu77J/GiHAECLlhbzJ4p39SXGyjVB3KrJu/9J2v1OPqFR5shOquEmyvGF3FIbCoVoAWI19UgCsRqQAWI1IAbAakQJgNSIFwGpECoDViBQAqxEpAFYjUgCs9j9qGEwTZwU5GgAAAABJRU5ErkJggg==)
Find the possible value of AC?
MathematicsGrade9
Mathematics
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find the possible values of x?
Apply the Hinge theorem and converse and solve the following.
![](data:image/png;base64,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)
Find the possible values of x?
MathematicsGrade9
Mathematics
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What is the possible measure of MN, if MP = 20?
The length of MN = 5x + 3
= 5(2) + 3 = 13
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What is the possible measure of MN, if MP = 20?
MathematicsGrade9
The length of MN = 5x + 3
= 5(2) + 3 = 13
Mathematics
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What is the possible measure of MP?
Therefore, the length of MP>48.
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What is the possible measure of MP?
MathematicsGrade9
Therefore, the length of MP>48.
Mathematics
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What can be the x-value?
X < 9
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What can be the x-value?
MathematicsGrade9
X < 9
Mathematics
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAU0AAAEaCAYAAACVewWLAAATKUlEQVR4nO3dvW7b2LrG8YfKXIrkgx34Bg6VG5BcZIqDtPs0Q6XadoBJdVLOrjKApS7WNHva7CZTSLyBmFdgJIDJfSnhOgVFWZZlW5T4sRb5/wEGbMsf9Nfj933XIukZY4wAAHvpNX0AAOASQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA0AaAAQhMACiA04YRkNpTnefI8T5Ow6aNBlxGacECojxfR+qX5F1ITzSE0Yb/wi+aS/OlSU1/S/IuITTSF0IT1wi9zSb7enI10cipJc1FsoimEJiwXKsvMNzrrS6OfA0m06GgOoQm75a35mzP1JWn0swJJmv+mWdLokaGjPGOMafoggMeEE0/j+e7H/Gms6/N+vQeEzqPShMVWrfkjos8LUWyiboQm7LVqzRUsZYzZeFpmLXr0WQtSEzUjNGGtcFVmBj+Pth4ZKVsPivSZ1ETNmGkCQAFUmgBQAKEJAAUQmgBQAKEJAAUQmgBQAKEJ63me1/QhAGs/NX0AwGPysDTG3HseaBKhCevsCsj8ecITTSM0YY19ApHwRNM4IwhO8zyP4EStqDTRmM0FnkODj3kn6kZoohFlBh0tO+pEaKJ2VbXUm+FJcKIqhCZqU1clSMuOKhGaqFwTAUbLjqoQmqhMk4G1/bkJT5SFLUeohK1zRVuPC+6g0kSpbK/omHfiWIQmSuFSENGy4xiEJo7icvAQnjgEoYmDtWU+yP5OFEFoorC2VmbMO7EPLkL8rESzoSfP23qahE0fWO3yr90Y09pQyb+2/GsFtlFp4lldrL62551pmhKikERoFhBoaa40avowatb1OV/+tfd6Pf348YPgBO35/uYa5635cKIwafp4qrXZiiOrNF+8eMH3BITmQaK5xoOJ2jjV7MLc8lBpmsoYQ3h2HKH5rL7Or806ROLlVL4k6Ua3Las2Ccv9bIYn36vuITQL6o/O9MaXpEjf4qaPphy04oehZe8mQvM5yUyTSai8qEzCj7qIJMnXy0GDx1UCWvHj0bJ3D6vne7iZjzWYb70y+KDzfiOHc7QubiGqWpqmkrJVdmMMW5RajErzOf1z/bkMVnNMSfIVTJeKr9zcfERlWS3mne3H9TQ7guqyflSd7URothxh2TzCs10IzZYiLO1DeLYDodlCrOLajVMy3UZotgjVpTuoOt1FaLYAYekuwtM9hKbDCMv2IDzdQWg6irllOzHvtB+h6Riqy/aj6rQboekIwrJ7CE87EZoOoBXvNlp2uxCaFqO6RI6q0x6EpoUISzyG8GweoWkRwhL7Ijybw6XhGrL9i84l21BEWZeg6/V6zMwLotJs0GZw8mPAoQ6tOllgOgyh2RACE2UrEp4E5uEIzZoxt0TVngpPZqHHIzRrxOwIddquJqkuy0Fo1oDqEk3JK0tJVJclITQrRFjCBgRnudhyVBG2EKFp+XaiHz9+rH8Xy7lLZqLZZCjP87Kn4URhUsohO4FKs2RUl7DBU/PL4xaDEs2GA11E268PtDRXcvPG1sVQaZYk/69LdYmmPbfgs7kxvvDiZPhxFZiBlrGRMbGmviTN9SUs4eAdQGgeibCEbfatIA8Jz+T2RpLkT99r1Jekvs7e+JKkm9tu9OiE5hEIS7RBWadkRt/iEo/KXoTmATarS6At0jQ9rGVf8V8OKjgq+/zU9AG4hEUetF2apuvnPc9ji9IOVJp7YG6JsoQTT5431Mz28V8yk6+HV0Hqn5xKkqLPCyWSlIT6uFpKPz3pN3OsNSM0n0FYojTJTL/NJflvdNaXsu073t1+x/xpUt8ydBLONNk4huFkloVh/0zZ+o6vabwx7xz9rECSogsNPE/eYKy5JPlTve/CfiMRmo9ibomyJYvPiiT5b85UXU2WB/FEz0ZvONFgfKH5xp7LaP5N2XJOvioe6fMi2Zh3jvUpXijw797HD6aKr88r/JrswkxzC3NLVCX+Fkny9eZsO16a2BieaPbbXJLkT2Ndn2fHlCTJOvz6Z2/kX0RZK35+vp53Zpvju3tKJpXmCnNLVCvUl7kknerh6G+u8Y5TEpPZ8H67Hk6yFrqMgWiy0OdIkj/Vn+d3B9Tvbxxc/0SnkhTl1WfmqM3xLUBoirklLBLNNR5krXX//EM2P5yPNQnzyjDQh/OHjfA6YL38FMeNIN41I42/KevKv+njvZnm5tsO9NKXpBvt2rde1v5O13Q6NJlbojbJrW4kyX+pu92MfZ1fm/U/7Hg51ercmlVIjXS1DCRJ83EWhv70fbltfDTfmmmOVXQd6tj9na7pZGjSisNG/VG+Yh1pfXLN6P3q3G5p9zx09b7n16vf5/xc8EDL1e+3uXoiZv2p4jy0V59ofsBJ5F1q2TsXmoQlGrFrPpjMNJmEyjvfZH0xDF/5yTXJ7O9ZhelnK9kXH0vajjR4mVW10TfF2YZLxd+yh445s6cLLXtnQpNWHDa6mY+z/Y6ep8E4W81W8EHZ2DLfOB7ow3U+3/xttTH+yPBc78OcazzIZqHj+fbqfqxvkbR78epprW7ZTctJMh34MuGAZZD9LgbLu9fFy8D4q99RyTfBdGnirbf3p9lr4qmfvV2wNMYsH3z8A47ITH1//TciPzDTeOPheJodmz818aMf43me5xlJJk3TYw/YCq29CDH7LWGbZDbU4CK6ty/SZmUfb1vuhNnK9py5JWzUP3sjXxvnbVst0eLzY5vxD9OWeWerQpO5JazWP9eHQFL0WQvbU3O9+T0/T74c+VXlXZ53tqI9pxUH7LfrNhwutuxOV5rst0RnhZOmj2Bvm3fF3A5GF/d3OnvBDle+wUCXPXeTt9zmxUD2efsmOdee04oDbjg0AG1v2Z0JTcIScENZoWdreFofmoQl4I4q2mvbwtPq0GRuCbij6nmkLfNOK0OT6hJwR52VoA1Vp1VbjthCBLglr/6MMbWEWClblJJQb1+9Um99tfxA09ho3490ZGjuupveUMONy13ti7AE3NJku3zwKZnhW/VOznR1fX0XktEfencyUbjnx6mg0owUzcca7Hn5Z059BNzy1Gb1uhW7BF2ot2dzyRjpl4Vu0/yK+avbGO/5OUsKzezeyMYYxdPs8vy6uX2y2qQVB9xTdzu+j71b9vAvzSUZ/aLF1UiD1eH3R//Qp69XGu359VR3RtDpyb37ID/2DbblGw9gP72eVUshD+w6vjRN9Z/4RpKRfvlZo73ryodKCs1IFwNPF/mL/lTx1n1Jtv8zUV0CqFJVM9dq/mVEFxoMZzvb87wdz9tzAKhDf3AqyZP++KJw77Xyh0qfaa7vhhddaPseUJvV5mZ4AkCZdlaZo9cKJHn6Q2eTUHGem0mot68aXT2/s+vOodttOVUn4JZ8g7l7Rvp16kuepD/OdNJbbZMcjHV1Xds+zVw208zCb7C6DWmw93vTsgPusP1Ok0/NMvv/+KrbxUTD4cZj/i+6XLxvdvXcD6b68P688PvlPwBOowTstnn9y6ZPayyqP/qkr6NPB7+/leee52z9TwbgPpvCs+ozlawOTYmqE3BJ01ciquPz271LVcw7AZfYPu8sg/WV5rY2/zCANqm7Za+ryrW+0txG1Qm4wcU7Te7DudCUaNkBlxx8GTdLORmaOcITcMfDeWei2dvNiwFPtIwPC9U6F6Ccm2k+pU0tANBmj59VFGiRftL4gNv+1hWaTlea26g6ATeki0Cbf6Zpeqvp0JOnuf4KVehyGnVvc2pVaEq07IALktsbSZJ/eavUGL148V8a/89/S550c5sUS82aVXcR4oZtnpJJyw7YLU3TVcsuRd9jSYOmD+lRras0t1F1Am64vfSzln1+pl5vv2KniTOQWh+aEi07UKrwrXq97bvQZk+T5d0l1pJwpreveuvHhpOp9lkc9y9vlab27u/sRGjmuPAxUJPwrU7OLnR1fRd40fy74lWk9k9Os9f9e6HESEpC/f4ukjHS6Ulf8p7f39nUee6dCs0cVSdwhNEnpalZFyHGLDXxPEmBXo8kT4lm/5xL5m6hxxijOH5/t5Vo9FqBPCl6l10MeDDWlTGSf6lfR/dvp2vb+eydDE2Jlh0oSzL7p+YyUvA6u8tjstC/I8n4l/rX+WAdgP3+5v1pR/p0u9Bk42LAfnCp268X61vrbrLplMzOhmaO8ASOkbfVvi5/HWULOfF3RTKSvuv3V97GTHOpe1nXH+nT13T9N3h9tTswN9lwSmbnQzPHvBMo7q7K/D+d97f+dqK55tHmi2d6G+5/L57n5G173eFJaG6h6gT2dbd4E2TDzPv8S92uZp/xdCjPk+ZFT/fZYXMBqIkrxROaO9CyA3sI/8qqzO3Fm8Hf5MuTou+Ks6Vxxd+VLQz9bfAwXB3Tqgt2VKXpwTNgn0SzVyd6d230yyLVp/HmivfdY/f/anxd3n7VxXODy2c0fkuNRj6rY6g6gS3h73oXGZn1NqNNfZ1/XehyOLx7vR+0IjAlKs3CuNEb0BwbQpNKsyBW2YFm2BCYEqF5MFp2oJtae2m4Omxefm7zZQDtRWiWgPAEqmVLay7RnpeKeSfQfoRmBZh3AuWxqcqUaM8rQ8sOtBOVZsVo2YF2ITRrQssOFGdbay7RnteKlh1wH6HZAMITeJ6NVaZEe94o5p2AewhNCzDvBNxBe24JWnbgjq2tuUSlaR1adsBuhKalaNnRVTZXmRLtudVo2QH7UGk6gJYdsAeh6RBadrSd7a25RHvuHFp2oFmEpqMIT7SNC1WmRHvuPOadQL0IzZZg3gnUg/a8RWjZ4SpXWnOJSrOVaNmB6hCaLUbLDhe4VGVKtOetR8sOlItKsyNo2YFyEJpVSUJNhllrPAl3PTZct87ecKIwqeewaNlhE9dac4n2vBLJbKjBRfTYgxoOLnTv0Wiu8d9fKr4+V7+G46NlBw5HpVm6RIvPUjBdaho88iZ+oGWctcvxcvVG0Wctaqo2c5stu0v/6dEOLlaZEpVmBfo6v76WJIWTXQ+fa/Vw9uLgpXxJkU51UkeZucNm5UnVCTyNSrNh4cesVfen7zVq+FioOoHnUWk2KJkNNZ5LCpb687yhMnML807UwdXWXKLSbMx6sShYKr4a1bIAVARblIDdqDRrl2g2HOgikvxprGtLKszHbAYnVSfK4HKVKUme4S+hZHehuC1YGl1pIm883/metoco4YkyuB6aVJrYG/NOgEoTR2CLEopyvcqUWAjCEdiihC6iPcdRaNmxrzZUmRKVJkrCFiV0BaGJUtGyo+1oz1E6WnZsa0trLlFpokK07GgjQhOVo2XvtjZVmRLtOWpCy462oNJErbjwcXv0er1OnuDAGUFoVBf/6Nrmqfa7ba25RKWJhlF1ui9NU7148aIz//ycrjSZj7ULP0+3bVeVbawyJYcXgmjr2od7FbktTVP1ej0ZY5SmadOHUxlnQ5M/qvbiwsfuysMyD882cjY00W5sUYKtWAiC1TiryF1tXSAiNOEEVtndsbkA1MbgJDThDDbGuykPzrYs8BGacA7h6Z40TWWMaUXVSWjCWcw77fPc3sw2tOusnsN5bFFyi+t7OAlNtAJblJrX1jOAttGeo1Vo2VE1QhOtxEIRqkJ7jtaiZa9PV1pzidBEBxCeKBPtOTqDeWc1ulRlSoQmOoh5J45Be45OomXHoag00Wm07MfpWmsuEZqAJFp27I/2HFihZS+mi1WmRKUJPEDLjqcQmsAjNlt2qk7kCE3gCXnV2aaL6Jahq625RGgCe9m8iC7h2W2EJlBAm65AfqguV5kSoQkcpG33vcH+CE3gQLTs3URoAkfqUsve9dZcIjSB0tCyd4Nn+OkCpev1ejLGKE3T1lRlVJkZKk2gAl1q2buG0AQqRMvePrTnQE1cbtlpze9QaQI1YYtSOxCaQM1cm3dSZd5HaAINYd7pJkITaBAtu3sITcACtrbstOYPEZqARWjZ7ceWI8BSTW9RosrcjUoTsBTzTjsRmoDlbJ13dhWhCTiiznknrfnjCE3AIbTszSM0AQdV2bJTZT6N0AQcxhal+hGagONo2etFaAItUUbLTmv+PEITaBla9mpxRhDQYkXOKqLK3A+VJtBizDvLR2gCHcBZReUhNIEOeWzeSWu+v5+aPgAA9UrTVNL9eSf2x0IQ0HFUmcXQngMdlleb9yWaveqp53nyNp6Gw4nCOGnkOG1CaAIdli8Q7VNlRtFc45OBJkujLrenhCaAR/i6vM1C1ZhYy8lQnqT52VuFHZ7qEZoA9tDX6NO/dDn05Gmuv0J1ttokNAHsqa+T0+y5m9vuzjYJTQAogNAEsKdEtzfZc6cn/WYPpUGEJoA9JArf/q/eXRsZBXo9krq6q5MzggA8ItK7k57ebb02WHzSqMMb4ak0AezBl+8HWt6muhp7na0yJU6jBIBCqDQBoABCEwAKIDQBoABCEwAKIDQBoABCEwAKIDQBoABCEwAKIDQBoABCEwAKIDQBoABCEwAKIDQBoID/B8Rk78JWP/RMAAAAAElFTkSuQmCC)
What is the possible measure of ∠ACB?
As
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
What is the possible measure of ∠ACB?
MathematicsGrade9
As
Mathematics
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
what can be the x value?
5x + 6 < 76
5x < 70
x < 14
Use the Hinge theorem and its converse and solve the following
![](data:image/png;base64,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)
what can be the x value?
MathematicsGrade9
5x + 6 < 76
5x < 70
x < 14
Mathematics
Write a contradictory assumption for “if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle.”
If in triangle XYZ , Y=60 and X=60, then triangle XYZ is not an equilateral triangle.
Write a contradictory assumption for “if in ∆XYZ, ∠X = 60°, ∠Y = 60°, then ∆XYZ is an equilateral triangle.”
MathematicsGrade9
If in triangle XYZ , Y=60 and X=60, then triangle XYZ is not an equilateral triangle.
Mathematics
Write the contradictory assumption for “if a and b are even numbers, then a + b is an even number.”
Write the contradictory assumption for “if a and b are even numbers, then a + b is an even number.”
MathematicsGrade9
Mathematics
What is the temporary assumption to prove that A is an obtuse angle by proof of contradiction?
What is the temporary assumption to prove that A is an obtuse angle by proof of contradiction?
MathematicsGrade9