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What is the missing reason in the proof?

What is the missing reason in the proof?-example-1
User CrazyPen
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2 Answers

6 votes

the answeris segment addition


User Ian Sudbery
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4 votes

Answer:

Option 2.

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.

User Hajin
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