Question

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent:

Answer 1

D) Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem.

Answer 2

Answer:

D. Angles BAC and DCA are congruent by the Alternate interior angles theorem.

Step-by-step explanation:

Given ABCD is a parallelogram.

AB=CD and BC=AD

$AB\parallel CD \; and\; BC\parallel AD$

To prove that $AB\cong CD\; and\; BC\cong AD$.

Proof: According to given information

$AB\parallel CD$ and segment $BC\parallel AD$.

Construct diagonal AC with a straightedge.

In $\triangle ABC\; and\; \triangle ADC$

AC=AC

Reflexive property of equality.

$m\angle BCA\cong m\angle DAC$

By alternate interior angles theorem.

$m\angle BAC\cong m\angle DCA$

By alternate interior angles theorem.

$\triangle BCA\cong\triangle DAC$

By ASA( Angle-Side_Angle) theorem.

By CPCTC opposite sides AB and CD, as well as BC and DA are congruent.

Hence proved.