Question

given abcd is a parallelogram. prove: ∠a≅∠c and ∠b≅∠d. by the definition of a ▱, ad∥bc and ab∥dc. using, ad as a transversal, ∠a and ∠ are same - side interior angles, so they are . using side as a transversal, ∠b and ∠c are same - side interior angles, so they are supplementary. using ab as a transversal, ∠a and ∠b are same - side interior angles, so they are supplementary. therefore, ∠a is congruent to ∠c because they are supplements of the same angle. similarly, ∠b is congruent to ∠ .

Explanation:

Step1: Identify same - side interior angles with AD as transversal

When AD is a transversal for parallel lines AB and DC, ∠A and ∠D are same - side interior angles. Since AB∥DC, same - side interior angles are supplementary.

Step2: Identify same - side interior angles with BC as transversal

When BC is a transversal for parallel lines AB and DC, ∠B and ∠C are same - side interior angles and they are supplementary. Also, when AB is a transversal for parallel lines AD and BC, ∠A and ∠B are supplementary.

Step3: Prove angle congruence

We know that ∠A+∠B = 180° and ∠B + ∠C=180°. So, ∠A=180° - ∠B and ∠C=180° - ∠B. Thus, ∠A≅∠C. Similarly, since ∠B+∠C = 180° and ∠C+∠D=180°, ∠B≅∠D.

Answer:

• Using AD as a transversal, ∠A and ∠D are same - side interior angles, so they are supplementary.
• Using side BC as a transversal, ∠B and ∠C are same - side interior angles, so they are supplementary.
• ∠A is congruent to ∠C because they are supplements of the same angle. Similarly, ∠B is congruent to ∠D.