Question

prove that the internal angle bisectors of all angles of a parallelogram form a rectangle

Answer 1

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