Question

"What are the missing reasons in the proof?

Answer 1

According to the theorem given in the question.The missing statements are in bold,given below.

Statements:
Line segment AB is parallel to line segment CD (missing:It is the property of parallelogram) 
Angle ABD is congruent to angle CDB (Missing : It is the reflexive property)

Triangle ABD is congruent to triangle CDB (Missing: ASA Property)

ASA refers to Angle Side Angle.
I hope its is helpful

Answer 2

Answer:

AB is ║ to CD( property of parallelogram)

∠ABD is congruent to ∠CDB( Angles opposite of equal sides are congruent)

BD=BD( Reflexive property),

Step-by-step explanation:

Given: ABCD is a parallelogram with diagonal line segment BD.

Proof: In ΔABD and ΔCBD,we have:

AB is parallel to CD( Property of paralleogram),

∠ABD is congruent to ∠CDB( Angles opposite of equal sides are congruent)

BD=BD( Reflexive property),

Therefore, ΔABD≅ ΔCBD,