Given: abcd is a kite.
prove: bd bisects ac.

what is the missing reason in step 5?

a. corresponding parts of congruent triangles are congruent

b. corresponding parts of similar triangles are congruent

c. diagonals of a kite are congruent

d. adjacent sides of a kite are congruent

statements

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 5. ?
6. bd bisects ac at point p 6. definition of bisect

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.

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

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

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step-by-step explanation:

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