Question

What is the missing reason in the proof?

Answer 1

Answer:

Option 2.

Step-by-step explanation:

Given information: ABCD is a parallelogram with diagonal BD.

Prove: ΔABD ≅ΔCDB

Proof:

Definition of parallelogram: Opposite sides of a parallelogram are parallel and congruent.

Alternate interior angle theorem : If a transversal line intersect two parallel lines, then the alternate interior angles are congruent.

ASA postulate: If two corresponding angles and their included side are congruent, then both triangles are congruent.

Statement                                     Reason

1. AD║BD                                 1. Definition of parallelogram.

2. ADB≅CBD                           2. Alternate interior angle theorem.

3. AB║CD                                 3. Definition of parallelogram.

4. ABD≅CDB                           4. Alternate interior angle theorem.

5. DB≅DB                                5. Reflexive property of congruence

6. ΔABD ≅ΔCDB                    6. ASA

The missing reason is "Definition of parallelogram".

Therefore, the correct option is 2.

Answer 2

the answeris segment addition