Question

Abcd is a parallelogram, p is the mid point of cd and cd = 2bc, find the measure of angle APB.

Answer 1

Answer:

90°

Explanation

Given,

P is mid point of CD

therefore CP = DP

CD = 2BC

therefore CP = CB

AB = CD, CB = AD ( opposite lines in a parallelogram are equal)

P is also mid point of AB (Let's take this P as P')

P'p = CB = AD = P'B = P'B

angle BP'P = 90°

angle AP'P = 90°

BPP' = PBP' = APP' = PAP' = 45° {Sum of angles in a triangle)

45 + 45 = 90°