In the parallelogram ABCD, bisectors of angles B and C are drawn, which intersect at point P

univerkov | September 9, 2021 | education

In the parallelogram ABCD, bisectors of angles B and C are drawn, which intersect at point P on the side of AD. Find the perimeter of the parallelogram if AB = 10 cm

1. The bisector BP of the parallelogram ABCD separates the triangle ABC from it, which is isosceles (according to the properties of the parallelogram). Therefore, AB = AP = 10 cm.

2.AB = CD = 10 cm.

3. The bisector CP of the parallelogram ABCD separates the triangle CDP from it, which is isosceles (according to the properties of the parallelogram). Therefore, CD = DP = 10 cm.

4. AD = AP + DP = 10 + 10 = 20 cm.

5. The sum of the angles of the parallelogram (perimeter) is 2 (AB + AD) = 2 (10 + 20) = 60 cm.

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