On the AD side of the parallelogram ABCD, point M is taken so that DM = DC a) prove that CM is the bisector

| August 14, 2021 | education

On the AD side of the parallelogram ABCD, point M is taken so that DM = DC a) prove that CM is the bisector of the angle C of the parallelogram b) find the perimeter of the parallelogram if AB = 8.5 cm, AM = 3.5 cm

1. According to the properties of the parallelogram, the bisector of one of the corners divides the parallelogram into two geometric shapes. One of them is an isosceles triangle.

Since, according to the condition of the problem, DM = CD, the triangle CDM is isosceles, that is, CM is the bisector ∠C, which was required to be proved.

2. According to the properties of the parallelogram, AB = CD = 8.5 cm and BC = AD.

3. Calculate the length of the side AD:

AD = AM + DM = 3.5 + 8.5 = 12 cm.

4. Calculate the total length of all sides of a given parallelogram (perimeter P):

P = 2СD + 2 АD = 8.5 x 2 + 12 x 2 = 17 + 24 = 41 cm.

Answer: the total length of all sides of the parallelogram (perimeter) is 41 cm.



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