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)

 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

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step-by-step explanation:

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