ABCD-parallelogram BE-bisector ∠ABC AE = 8 cm AD = 2 cm Find the perimeter of the parallelogram.

univerkov | August 22, 2021 | education

Since BE = bisector of angle ABC, then angle ABE = CBE.

In a parallelogram, the opposite sides are equal and parallel, then the angle CBE = AEB as the intersecting angles at the intersection of parallel lines AD and BC secant BE, and then the angle ABE = AEB, and therefore the triangle ABE is isosceles. Then AB = AE = 8 cm.

Side length AD = AE + ED = 8 + 2 = 10 cm.

Determine the perimeter of the parallelogram.

Ravsd = 2 * (AB + AD) = 2 * (8 + 10) = 2 * 18 = 36 cm.

Answer: The perimeter of the parallelogram is 36 cm.

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