CBSE Class 9 Answered
Prove that the angle bisectors of a parallelogram form a rectangle.
Asked by Topperlearning User | 16 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 | 16 Aug, 2017, 05:14: PM
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