Question

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

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

The correct option is A which is ''If two triangles are congruent then their corresponding parts are congruent''.

Given: ABCD is a kite.

To Prove: BD bisects AC.

What is the definition of the kite?

The kite's sides, angles, and diagonals all have to identify properties.

To be a kite, a quadrilateral must have two pairs of sides that are equal to one another and touching.

This makes two pairs of adjacent, congruent sides.

AB ≅ BC, BP ⊥ AC

Reflexive property; the reflexive property is known as the reflexive property of congruence.

BP ≅ BP

The HL Theorem states; If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

△ABP ≅ △CBP

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

AP ≅ CP

Bisect means to cut or divide into two equal parts.

BD bisects AC at point P.

Hence proved.

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