Question

In figure AB = CB and ∠ADC = ∠AEC = 70°. Is AE = CD? Why?​

Answer 1

Step-by-step explanation:

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In the given figure, if x=y and AB=CB then prove that AE=CD.

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Solution

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It is given that x=y and AB=CB

By considering the △ABE

We know that

Exterior ∠AEB=∠EBA+∠BAE

By substituting ∠AEB as y we get

y=∠EBA+∠BAE

By considering the △BCD

We know that

x=∠CBA+∠BCD

It is given that x=y

So we can write it as

∠CBA+∠BCD=∠EBA+∠BAE

On further calculation, we can write it as

∠BCD=∠BAE

Based on both △BCD and △BAE

We know that B is the common point

It is given that AB=BC

It is proved that ∠BCD=∠BAE

Therefore, by ASA congruence criterion we get

△BCD≅△BAE

We know that the corresponding sides of congruent triangles are equal

Therefore, it is proved that AE=CD.