If in Fig. 6.11, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m

Solution:

Given, bisectors AP and BQ of the alternate interior angles are parallel.

We have to show that the lines l and m are parallel.

Given, AP and BQ are parallel.

We know that if a transversal intersects two parallel lines, then alternate interior angles are equal.

The alternate interior angles are ∠CAB and ∠ABF

As AP || BQ and t is transversal

∠PAB = ∠ABQ

Let us multiply 2 on both sides

2 ∠PAB = 2 ∠ABQ

As the alternate interior angles are equal, the lines are parallel

Therefore, the lines l and m are parallel.

✦ Try This: In the given figure , the arms of two angles are parallel. If ∠ABC=70°, then find ∠DEF

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6

NCERT Exemplar Class 9 Maths Exercise 6.3 Problem 4

If in Fig. 6.11, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m

Summary:

Alternate interior angles are the angles formed on the opposite sides of the transversal. If in Fig.6.11, bisectors AP and BQ of the alternate interior angles are parallel, then it is shown that l || m

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