Question 4 In the given figure, bisectors AP and BQ of the alternate interior angles are parallel, then show that l||m.
Open in App
Solution
Given, AP || BQ, AP and BQ are the bisectors of alternate interior angles ∠CABand∠ABF. To show I||m, Proof: Since, AP || BQ and t is transversal, therefore ∠PAB=∠ABQ. [alternate interior angles] ⇒2∠PAB=2∠ABQ [multiplying both sides by 2]
⇒∠CAB=∠ABF So, alternate interior angles are equal. We know that, if two alternate interior angles are equal, then lines are parallel. Hence, I || m.