Question

What other information do you need to prove ΔABE is congruent to ΔEDA by SSS?

A) A= C
B) ΔEAC is isosceles triangle with base EC
C) E= C
D) EAC is equilateral triangle

Answer 1

Eother B or D

But my answer is triangle ACE is an isosceles triangle not EAC

Answer 2

D) EAC is equilateral triangle

Explanation:

Given :

AEC is a triangle in which B∈ AC and D∈EC

Such that,

∠ABE = 90°,

∠ADE = 90°,

Also, BC = CD

We have to prove that :

Δ ABE is congruent to Δ EDA

Proof :

If EAC is an equilateral triangle,

By the property of equilateral triangle,

EA = AC = EC

If AC = EC

⇒ AB + BC = ED + CD

⇒ AB + CD = ED + CD

⇒ AB = ED

Also, AE = AE ( common segment )

Now, if in two right triangles hypotenuse are equal and any corresponding legs are equal,

Then, the other legs must be equal,

That is, BE = DA,

Hence, by SSS postulate of congruence,

Δ ABE ≅ Δ EDA

Therefore, option D is correct.