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.
