Question

Given parallelogram ABCD, explain how to prove that Angles B and D are congruent. Stating that the angles are automatically congruent because it is a parallelogram is not sufficient.

Answer 1

To prove that angles B and D in parallelogram ABCD are congruent, use the property that opposite angles in a parallelogram are always congruent.

Step-by-step explanation:

To prove that angles B and D in parallelogram ABCD are congruent, you can use the property that opposite angles in a parallelogram are always congruent. Here is a step-by-step explanation:

1. Start by drawing the given parallelogram ABCD.
2. Draw a diagonal AD from vertex A to vertex D.
3. Since opposite angles in a parallelogram are congruent, we know that angle A and angle C are congruent.
4. By transitive property of congruence, if angle A is congruent to angle C, and angle A is opposite to both angles B and D, then angle B and angle D must be congruent as well.

Therefore, angles B and D in parallelogram ABCD are indeed congruent.