Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
in Plane Geometry and Line and Angle by (34k points)
closed by

If a transversal intersects two parallel lines l and m then prove that the bisectors AP and BQ of any two alternate angles are parallel i.e. AP || BQ.

1 Answer

+1 vote
by (31.3k points)
selected by
Best answer

Given: l || m and a transversal intersect these two parallel lines at A and B respectively.

AP and BQ are the bisectors of two alternate angles

To prove: AP || BQ

Proof: ∵ l || m (given)

⇒ ∠1 = ∠2

(alternate interior angles)

⇒ \(\frac { 1 }{ 2 }\)∠1 = \(\frac { 1 }{ 2 }\)∠2

⇒ ∠PAB = ∠QBA

Hence, the two lines AP and BQ are intersected by a transversal AB forming a pair of alternate angles equal.

∴AP || BQ Hence proved

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.