Question

Match the reasons with the statements in the proof to prove that BC = EF, given that triangles ABC and DEF are right triangles by definition, AB = DE, and A = D.

Given:


ABC and DEF are right triangles


AB = DE


A = D


Prove:


BC = EF


1. ABC and DEF are right triangles


AB = DE


A = D CPCTE (Corresponding Parts of Congruent Triangles are Equal)

2. ABC ≅ DEF Given

3. BC = EF LA (Leg - Angle)

Answer 1

Answer: Statement Reason

1. ABC and DEF are right triangles 1. Given

AB = DE , ∠A = ∠D

2. Δ ABC ≅ Δ DEF 2. LA(Leg - Angle)

3. BC = EF 3. CPCTE(Corresponding

Parts of Congruent

Triangles are Equal)

Explanation:

Here, Given: ABC and DEF are right triangles.

AB = DE and ∠A = ∠D

Prove: BC = EF

Since, AB = DE and ∠A = ∠D

That is, leg and an acute angle of right triangle ABC are congruent to the corresponding leg and acute angle of right triangle DEF,

Therefore, By Leg angle theorem,

Δ ABC ≅ Δ DEF

⇒ BC ≅ EF ( by CPCTC )

⇒ BC= EF