Question

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

Answer 1

Answer:

here's your answer...

Answer 2

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 = 180degree (sum of consecutive interior angles is 180degree)

MLS + LMS = 90degree

In LMS, MLS + LMS + LSM = 180degree

90degree + LSM = 180degree

LSM = 90degree

Hence, RSP = 90degree (vertically opposite angles)

Similarly, SRQ = 90degree, RQP = 90degree and SPQ = 90degree

Hence, PQRS is a rectangle.