Question

Given: ABCD is a kite.

Answer 1

Answer :- A. Corresponding parts of two congruent triangles are congruent.

Complete proof :-

    Statement                        reasons

1. ABCD is a kite          1. given

2. AB ≅ BC, BP ⊥ AC          2. definition of kite

3. BP ≅ BP                          3.  reflexive property

4. △ABP ≅ △CBP          4. HL theorem

5. AP ≅ CP are congruent  5. Corresponding parts of two congruent    

                                                            triangles

6. BD bisects AC at point P 6. definition of bisect

• If two triangles are congruent then their corresponding parts are congruent.

So, option A must be the reason for step 5 which completes the proof.

Answer 2

Consider ΔABP and ΔCBP. They have:

1. AB ≅ BC (by definition of kite);

2. BP ≅ BP (by reflexive property);

3. BP ⊥ AC (by definition of kite).

Then these two triangles are congruent be HL theorem.

Corresponding parts of congruent triangles are congruent (by definition of congruent triangles), then the correct choice for step 5 is A.