Question

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

Answer 1

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

Step-by-step explanation:

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

MLS + LMS = 90o

In LMS, MLS + LMS + LSM = 180o

90o + LSM = 180o

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