In parallelogram ABCD, the bisector of an acute angle C intersects side AD at point M.

univerkov | July 4, 2021 | education

In parallelogram ABCD, the bisector of an acute angle C intersects side AD at point M. AM = 2 cm, MD = 8 cm. Find the perimeter of a parallelogram ABCD

1. According to the properties of the parallelogram, the bisector CM separates the isosceles triangle CDM from the parallelogram.

Therefore, DМ = СD = 8 centimeters.

2. AD = AM + DM = 2 + 8 = 10 centimeters.

3. We calculate the perimeter of the parallelogram, equal to the total length of all its sides, taking into account that the opposite sides of this geometric figure are equal:

2 (CD + AD) = 2 (8 + 10) = 36 centimeters.

Answer: The perimeter of the parallelogram is 36 centimeters.

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