Question

Figure ABCD is a parallelogram.

Answer 1

Answer is

A. First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles.

hope it helps

Answer 2

Answer:

Option A is correct.

First prove ABC is congruent to CDA and then state AD and BC are corresponding sides of the triangles.

Step-by-step explanation:

Given the figure: ABCD is a parallelogram.

Parallelogram states that the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

therefore, AB is parallel to CD    [by definition of parallelogram]

here, in the figure, AC becomes a transversal line.

let $\triangle CDA$ and $\triangle ABC$

Alternate angle property states that the two angles are on opposite sides of the sloping transversal line.

$\angle DAC = \angle BCA$  [Angle]     [By property of alternate angle]

AC = AC       [Common side]

$\angle ACD = \angle BAC$  [Angle]       [By property of alternate angle]

ASA (Angle-Side-Angle) Postulates states that if two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

therefore, by ASA postulates;

$\triangle CDA \cong \triangle ABC$

Then, by CPCT [ Corresponding part of the congruent triangle]

AD = BC         hence proved!