Question

In parallelogram KLMN, where KN is parallel to LM and KL is parallel to MN, prove that ∠N is congruent to ∠L and ∠M is congruent to ∠K.

Answer 1

To prove that angle N is congruent to angle L in parallelogram KLMN, we need to show that the corresponding sides are parallel and equal in length.

Step-by-step explanation:

To prove that angle N is congruent to angle L in parallelogram KLMN, we need to show that the corresponding sides are parallel and equal in length. Since KN is parallel to LM and KL is parallel to MN, we can use the properties of a parallelogram to prove the congruence.

First, consider the opposite sides KN and LM. These sides are parallel because they never intersect. Next, we look at the opposite sides KL and MN. Again, these sides are parallel because they never intersect. Therefore, we have established that the corresponding sides are parallel.

Now, we need to show that the corresponding sides are equal in length. Since the opposite sides of a parallelogram are equal in length, we know that KL = MN and KN = LM. Therefore, we can conclude that angle N is congruent to angle L in parallelogram KLMN.