The bisector of the angle M, the parallelogram MNPA intersects the side at the point C

univerkov | August 10, 2021 | education

The bisector of the angle M, the parallelogram MNPA intersects the side at the point C, NC = 2.4 cm, CP = 6.6 cm. Find the perimeter

Let us determine the length of the HP side. НР = НС + СР = 2.4 + 6.6 = 9 cm.

Since the MC is the bisector of the angle AMH, the angle HMC = AMC.

Opposite sides of the parallelogram are parallel, then the angle MCH = AMC as crosswise lying angles at the intersection of parallel lines AM and HP secant MС.

Then the angle MCH = HMC, which means that the triangle MНC is isosceles, MH = HC = 2.4 cm.

Determine the perimeter of the parallelogram.

Rmnra = 2 * (MH + HP) = 2 * (2.4 + 9) = 22.8 cm.

Answer: The perimeter of the parallelogram is 22.8 cm.

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