MediumGeometry
Why does a parallelogram's angle bisector form an isosceles triangle?
TL;DR
KM = ME, so triangle KME is isosceles.
Question
In parallelogram KMNR, the bisector of angle MKR meets side MN at E. Prove that triangle KME is isosceles.
Answer
KM = ME, so triangle KME is isosceles.
Explanation
KE bisects angle MKR, and ME is parallel to KR. Therefore ∠MKE = ∠KEM, so their opposite sides ME and KM are equal.
