In the KMNP parallelogram, the correct bisector of the MKP angle that intersects the MN side at point E

In the KMNP parallelogram, the correct bisector of the MKP angle that intersects the MN side at point E a) Prove that the KME triangle is isosceles b) find the KP side if ME 10 cm, P parallelogram = 52 cm

1. Let us denote the angle by the symbol ∠.

2. ∠МКЕ = ЕКР, since the bisector КЕ divides ∠К into two equal parts.

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

4. ∠MKE = ∠MEK. Therefore, the triangle KME is isosceles. ME = KM = 10 cm.

5. We calculate the length of the KP using the formula for calculating the perimeter of a triangle:

2 (KM + KР) = 52 cm.

KM + KР = 26 cm.

KР = 26 – KM = 26 – 10 = 16 cm.

Answer: the length of the side of the KР is 16 cm.