Question

Given:

ABCD is

Prove:
A = C

Which of the following statements must be included in this proof?

Triangle ABD congruent to Triangle CDB
Triangle ABC congruent to Triangle CDA
Angle B congruent to angle D

Answer 1

ABD congruent to CDB

Answer 2

Explanation:

Given: ABCD is a parallelogram.

To prove: ∠A=∠C

Solution:

It is given that ABCd is a parallelogram, then

From ΔABD and ΔCDB, we have

AB=CD(Opposite sides of parallelogram are equal)

AD=CB (Opposite sides of parallelogram are equal)

BD=BD (Common)

Thus, by SSS rule of congruency,

ΔABD≅ΔCDB

Therefore, by CPCTC, we have

∠A=∠C

Hence proved.