Question

Line-segments AB and CD bisect each other at O. AC and BD are joined forming triangles AOC and BOD. State the three equality relations between the parts of the two triangles, that are given or otherwise known. Are the two triangles congruent? State in symbolic form. Which congruence condition do you use?​

Answer 1

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Line-segments AB and CD bisect each other at O. AC and BD are joined forming triangles AOC and BOD. State the three equality relations between the parts of the two triangles, that are given or otherwise known. Are the two triangles congruent? State in symbolic form. Which congruence condition do you use?

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Solution

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Let, this be figure of given condition.

In figure, line segments AB and CD bisect each other at O.

So, O is midpoint of CD and AB

Therefore,

OC=OD

OB=OA

and ∠AOC≅∠BOD⋯⋯[vertically opposite angles]

Hence, by SAS test we can say that

ΔAOC≅ΔBOD

So, yes two triangles are congruent.

Congruence condition used is SAS

Above written two pairs of equal sides and one pair of equal angles are three equality relations of matching parts used to arrive at answer.

Answer 2

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