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: 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)

Step-by-step 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