In the parallelogram ABCD, the angle B is equal to 120 ° and the bisector of this angle is lemm side AD

| March 25, 2021 | education

In the parallelogram ABCD, the angle B is equal to 120 ° and the bisector of this angle is lemm side AD to the segments AE 6 cm and DE 2 cm. Find: a) the angles of the parallelogram: the perimeter of the parallelogram. b) Determine the species …

The sum of the adjacent angles of the parallelogram is 180, then the angle BAD = BCD = 180 – 120 = 60.

Since AE is the bisector of the angle ABC, then by the property of the bisector, it cuts off the isosceles triangle ABE, and since the angle ABE = ABC / 2 = 120/2 = 60, then the triangle ABE is equilateral AB = AE = BE = 6 cm.

Side length AD = AE + DE = 2 + 6 = 8 cm.

Since the opposite sides of the parallelogram are equal, AB = CD = 6 cm, BC = AD = 8 cm.

The perimeter of the parallelogram is: P = 2 * (AB + AD) = 2 * (6 + 8) = 28 cm.

The quadrilateral BCDE is an isosceles trapezoid, since BC is parallel to DE, and BE = CD.

Answer: The angles of the parallelogram are 60 and 120, the perimeter is 28 cm, BCDE is an isosceles trapezoid.



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