In the parallelogram KMNP, the bisector of the angle K is drawn which intersects the side MN at point E

In the parallelogram KMNP, the bisector of the angle K is drawn which intersects the side MN at point E a) prove that the triangle KME is isosceles b) find the side KP if ME = 10cm, and the perimeter of the parallelogram is 52cm

a). The bisector КЕ is a secant for parallel lines КР and МN.

The angles PKE and KEM are crosswise, which means <PKE = <KEM.

<ЕKР = <EKM, so <EKM = <KEM.

These are the angles at the base of the KME triangle, which means it is isosceles;

b). KM = EM = 10 cm;

KMNP parallelogram perimeter:

P = 2 * (KP + KM);

KP = P / 2 – KM = 52: 2 – 10 = 16 (cm).