Given a parallelogram MNVB. The bisector of angle N intersects MNB at point A. MA = 4cm, AB = 6cm.

univerkov | February 15, 2021 | education

Given a parallelogram MNVB. The bisector of angle N intersects MNB at point A. MA = 4cm, AB = 6cm. Find the perimeter of the NMVB.

A parallelogram has opposite sides equal and parallel.

Then the angle МАN = ANV as the cross-lying angles at the intersection of parallel lines MB and NV secant АN, then the angle МNA = МАN, since NA is the bisector of the angle МNV.

Then in the MNA triangle the angles at the base NA are equal, and then the MNA triangle is isosceles, MN = MA = 4 cm.

Then VB = MN = 4 cm.

The length of the segment MV = MA + AB = 4 + 6 = 10 cm, NV = MA = 10 cm.

Determine the perimeter of the parallelogram MNVB.

P = 2 * (MN + MB) = 2 * (4 + 10) = 28 cm.

Answer: The perimeter of the parallelogram is 28 cm.

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