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# If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form

a. a square

b. a rhombus

c. a rectangle

d. any other parallelogram

**Solution:**

Consider the bisectors of angles APQ and CPQ meet at the point M and the bisectors of angles BPQ and PQD meet at the point N

Now join PM, MQ, QN and NP

As APB || CQD

∠APQ = ∠PQD

As NP and PQ are angle bisectors

2∠MPQ = 2 ∠NQP

Let us divide both sides by 2

∠MPQ = ∠NQP

PM || QN

In the same way,

∠BPQ = ∠CQP

PN || QM

So PNQM is a parallelogram

We know that angles on a straight line is 180°

∠CQP + ∠CQP = 180°

2∠MPQ + 2∠NQP = 180°

By dividing both sides by 2

∠MPQ + ∠NQP = 90°

∠MQN = 90°

So PMQN is a rectangle.

Therefore, the bisectors of the angles APQ, BPQ, CQP and PQD form a rectangle.

**✦ Try This: **If DPE and FQH are two parallel lines, then the bisectors of the angles DPQ, EPQ, FQP and PQH form a. a square, b. a rhombus, c. a rectangle, d. any other parallelogram

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 8**

## If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form , a. a square, b. a rhombus, c. a rectangle, d. any other parallelogram

**Summary:**

If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form a rectangle

**☛ Related Questions:**

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