Prove the Following:

Question

In the plane figure on the left above, GE = KE, GM = KM, and H lies on line EM. Prove that GH = KH, without using congruent triangles.

Answer 1

EM is the perpendicular bisector of GK because E and M are both equidistant from its endpoints

Therefore H is also equidistant from the endpoints G and K.