Maths-
General
Easy
Question
In the figure, OA = OD and OB = OC. Show that:
(i) AOB ⩭ DOC
(ii) AB || CD
![](data:image/png;base64,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)
Hint:
Find the congruence rule used and then find the parallel sides.
The correct answer is: AB || CD.
(i) In ΔAOB and ΔDOC, we have
AO = OD (given)
BO = OC (given)
Since CB and AD intersects, we have
(vertically opposite angles)
So by SAS congruence rule, we have
ΔAOB ⩭ ΔDOC
(ii)Since ΔAOB ⩭ ΔDOC, we have
( Corresponding part of congruent triangles)
But they form alternate interior angles and since they are equal , AB || CD.
Related Questions to study
Maths-
If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that ![straight angle D A Q equals straight angle C B P](data:image/png;base64,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)
![](data:image/png;base64,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)
If AD ⟂ CD and BC ⟂ CD , AQ = PB and DP = CQ. Prove that ![straight angle D A Q equals straight angle C B P](data:image/png;base64,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)
![](data:image/png;base64,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)
Maths-General
Maths-
Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii) AD || BC
![](data:image/png;base64,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)
Prove that the medians bisecting the equal sides of an isosceles triangle are also equal. If OA = OB and OD = OC, show that:
(i) AOD ⩭ BOC
(ii) AD || BC
![](data:image/png;base64,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)
Maths-General
Maths-
Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?
Kumar wants to spread a carpet on the floor of his classroom. The floor is a square
with an area of 4160.25 square feet. What is the length of carpet on each side?
Maths-General
Maths-
The volume of a cubical box is 12167 cm3. Find the side of the box and its 6 sides area?
The volume of a cubical box is 12167 cm3. Find the side of the box and its 6 sides area?
Maths-General
Maths-
The area of a square is 289 m2, find its perimeter?
The area of a square is 289 m2, find its perimeter?
Maths-General
Maths-
What is the least seven digits which is a perfect square. Also find the square root of the number so obtained
What is the least seven digits which is a perfect square. Also find the square root of the number so obtained
Maths-General
Maths-
Find the least number which must be subtracted from 23416 to make it a perfect square.
Find the least number which must be subtracted from 23416 to make it a perfect square.
Maths-General
Maths-
Find the least number which must be added to 732733 to obtain a perfect square.
Find the least number which must be added to 732733 to obtain a perfect square.
Maths-General
Maths-
In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:
![](data:image/png;base64,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)
In the given figure, PQ || RS. Check whether ΔPOQ i congruent to ΔSOR Give reason for your answer:
![](data:image/png;base64,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)
Maths-General
Maths-
Show that 64 is square as well as cube number
Show that 64 is square as well as cube number
Maths-General
Maths-
From the given figures, find by which criteria the two triangles ABC and PQR are congruent.
In the figure XY = PZ. Prove that XZ = PY.
In the figure XY = PZ. Prove that XZ = PY.
![](data:image/png;base64,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)
From the given figures, find by which criteria the two triangles ABC and PQR are congruent.
In the figure XY = PZ. Prove that XZ = PY.
In the figure XY = PZ. Prove that XZ = PY.
![](data:image/png;base64,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)
Maths-General
Maths-
Evaluate: ![cube root of 3375](data:image/png;base64,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)
Evaluate: ![cube root of 3375](data:image/png;base64,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)
Maths-General
Maths-
Evaluate: ![cube root of fraction numerator left parenthesis negative 1728 right parenthesis over denominator 2744 end fraction end root](data:image/png;base64,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)
Evaluate: ![cube root of fraction numerator left parenthesis negative 1728 right parenthesis over denominator 2744 end fraction end root](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAtCAYAAAAjkQw8AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAc1CXO0QAABA5JREFUeNrtWm9klVEYP+aamUkpWvpwk2RmZtSHzcRmpA/7MDFtKpYyk0kfkn2JyDQrYsUkSVJRaUkqzUwmM7LSSF9WEiWl2Zq61nR7Hj1Xp3fnvO/z3nvOuZt7fvy4773Pfc89v/s+f845jxDxUAZMe+bEWKgCvhMeztACfORlcIejwEGm7WFgX4Ho0kfzNY7zwGMMu2rgeIE9jM9o3kYxCtzFHLzG0sS2Ak8AX2o+5yateuAd4Bxwge63V3PPUuAAcB6YAj4GbgzYbAOOmZ4sJsyKCJsaEtwWrgE7s8j4rcBL0vVTYDtVXohK+t3tiu9eBvYCE8BiCiETCrsxEt4ISoC/aNAw9AO7HbhwHMHXkxglEXZJ4CvF+6nAdRF5RRBHTOatWuAUww7dbccyE/x+jBCXUrw3L3lCRvAPCrs64IipCbYBbzPs5sjtlovgXRTzOajThMMBenplu7MKu2KavxH0AM8w7BYdVQUcwZMUaxMM2xKyrddUXQtEjP2fQrx4wdQEB5mxeZEhlInlL8cOxWlk2K0B3gPu1Pxp14EbJM/FxDitKQONCY5Jp2EFhRSsSh4y7rOZxN6i+fyuRthGKpOthZQZYDnDbljjli4Fx6T2hpEoK6hULI2ZRHWfsZNmxpUzC4Cga60GfmcKsRzKwhYKJ1Gl4i1GfH+teforKZbL6Kb5xwL+6+8Vi5kp5vdtL3w4gt8EHoj4/gPGIg6xm0RvJM8potfTVAHlvPDBG34LvNdBKzwuxm3sK4Qk3SA+UyLMNnmr8sEkRYAUeU+LiaX9WuAFxdNxEngqxn385lWMJ2e/Zv+iI+YP6BKFsz3bT/s7sbGKNmk6FSGiQXhYQ7Dc+UmViocF4JL1uXRdrih/PAxl/szmelL6rJaRAP1pvKFTesQh8f/GvYfhujaIc4J3jumRBZ6IpWd1Q4oi38MQfoilx/0vhL0D4YLHW+AN6Ro3dmZ8SWgPQ7RRk8Em4a61jdu2kG1V0MysGrh2RnAcOCtd4+py1NHYcdoWVGgNqabK6EGKEpJrZwxJGiwh7YcM5tHjdG0LQUS1QVwEHmQIybUzCjyTbKLX2NrWLfKLFMMmrA0CQ9WIFI5EjnbG8ZFqbwS2RbTlUWxd24KMsDaIYvKQZISQXDsrGBP/NtLxlKcqT2KHtS3IISesDaIv4KHpHO2s4DTwK73mtLbZQFjbQjDR6togqhXekc7BzhqaKI5jSfglD2JHtS3IVUlYG8SE4h7pHOys4rf423w/7HhcTtsCgtMGwa3Xje/2ZYNZctcrDsXmti0IwWuD0P0JJu2MYZIG7XE4JrdtAcFpg1hRgl+lQZsdjhnHrTltECtK8D006Hbh4QTrSPAyL4U7DHkJ3GKfl8AtfDixgD/YzMV+TraAiQAAALN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXJvb3Q+PG1mcmFjPjxtcm93Pjxtbz4oPC9tbz48bW8+JiN4MjIxMjs8L21vPjxtbj4xNzI4PC9tbj48bW8+KTwvbW8+PC9tcm93Pjxtbj4yNzQ0PC9tbj48L21mcmFjPjxtbj4zPC9tbj48L21yb290PjwvbWF0aD540t0UAAAAAElFTkSuQmCC)
Maths-General
Maths-
In the figure above,
and BC = XZ. What additional information is required to make ABC ⩭ YXZ by RHS congruence condition?
![](data:image/png;base64,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)
In the figure above,
and BC = XZ. What additional information is required to make ABC ⩭ YXZ by RHS congruence condition?
![](data:image/png;base64,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)
Maths-General
Maths-
Find the square-root of the following numbers.
b) 25921
Find the square-root of the following numbers.
b) 25921
Maths-General