In the parallelogram KMHP, the bisector of the angle MKP is drawn, which intersects the side MH at point E.

In the parallelogram KMHP, the bisector of the angle MKP is drawn, which intersects the side MH at point E. a) Prove that the triangle KME is isosceles. b) find the perimeter of KMHP, if ME = 10 cm, EH = 6 cm

Since KE is the bisector of the angle MKP, then the angle MKE = PKE.

Parallelogram has opposite sides parallel, КН || KP, then the angle PKE = KEM as criss-crossing angles at the intersection of parallel MH and KP secant KE.

Then in the triangle KME the angles MKE = KEM, and therefore the triangle KME is isosceles, as required.

Since KME is isosceles, KM = ME = 10 cm, MH = ME + HE = 10 + 6 = 16 cm.

Then Ркмнр = 2 * (КМ + МН) = 2 * (10 + 16) = 2 * 26 = 52 cm.

Answer: The perimeter of the parallelogram is 52 cm.