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

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

1. Let’s denote the angle by the symbol ∠.

2. ∠ЕКМ = ∠ЕКР, since the bisector AP divides ∠К into two equal parts.

3. ∠ЕКР = ∠ МЕК as internal criss-crossing at parallel sides МN and КР and

bisector КЕ intersecting them. 4. The angles adjacent to the KE side are equal. Hence,

triangle KME is isosceles. ME = KM = 10 cm.

4. Considering that the opposite sides of the parallelogram KMNP are equal, its perimeter

calculated by the formula:

2KM + 2KP = 52 cm.

KM + KP = 26 cm.

5.KR = 26 – 10 = 16 cm.

Answer: KP = 16 cm.