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

| August 2, 2021 | education

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

Since KE is the bisector of the MKR angle, the MKE angle = EKP.

The angle EKR is equal to the angle MEK as the intersecting angles at the intersection of parallel lines KP and MN secant KE, then the angle MKE is equal to MEK, and therefore the MKE triangle is isosceles, MK = ME = 10 cm.

Let the length of the segment EN be equal to X cm, then the length of the side MN = KP = (10 + X) cm.

The perimeter of the parallelogram is: P = 2 * (KM + KP) = 2 * (10 + 10 + X) = 52 cm.

2 * X + 40 = 52.

X = (52 – 40) / 2 = 6 cm.

Then KP = 10 + 6 = 16 cm.

Answer: The length of the side of the KP is 16 cm.



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