In the parallelogram KLMN, the current E is the middle of the KN side.

| February 27, 2021 | education

In the parallelogram KLMN, the current E is the middle of the KN side. It is known that EL = EM. Prove that the given parallelogram is a rectangle.

Let us prove that triangle KLE is equal to triangle MNE.

LK is equal to MN as opposite sides of the parallelogram, KE is equal to EN, and LE is equal to ME by condition. Then the triangles LKE and MNE are equal on three sides.

In equal triangles, the angles at the respective sides are equal. Angle LKE = MNE. Since the angles LKE and MNE are one-sided angles at the intersection of parallel lines LK and MN of the secant KN, their sum is 180. LKE + MNE = 180.

2 * LKE = 180.

LKE = MNE = 180/2 = 90.

Since in a parallelogram the opposite angles are equal, the parallelogram is a rectangle, which is what we had to prove.



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