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The figure shows two parallel lines AB and DE cut by the transversals AE and BD:

Which statement best explains the relationship between Triangle ABC and Triangle EDC ?

The figure shows two parallel lines AB and DE cut by the transversals AE and BD: Which-example-1

1 Answer

3 votes

Answer:
\triangle ABC\sim \triangle EDC

That is, triangles ABC and EDC are similar.

Explanation:

Given :
AB\parallel DE

AE and BD are the common transversal of the parallel lines AB and DE,

Then By the alternative interior angle theorem,


\angle BAC\cong \angle DEC

And,
\angle ABC\cong \angle EDC

Thus, By AA similarity postulate,


\triangle ABC\sim \triangle EDC

triangles ABC and EDC are similar.

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