Prove that the angle bisectors of a parallelogram form a rectangle.

Asked by Topperlearning User | 16th Aug, 2017, 03:14: PM

Expert Answer:

LMNO is a parallelogram in which bisectors of the angles L, M, N, and O intersect at P, Q, R and S to form the quadrilateral PQRS.
LM || NO                     (opposite sides of parallelogram LMNO)
L + M = 180o      (sum of consecutive interior angles is 180o)

MLS + LMS = 90o
In  LMS,  MLS + LMS + LSM = 180o
         90o + LSM = 180o
         LSM = 90o
Hence,    RSP = 90o               (vertically opposite angles)
Similarly, SRQ = 90o, RQP = 90o and  SPQ = 90o
Hence, PQRS is a rectangle.

Answered by  | 16th Aug, 2017, 05:14: PM