Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
8.8k views
in Lines and Angles by (47.3k points)
closed by

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

1 Answer

+1 vote
by (49.8k points)
selected by
 
Best answer

Let,

AB ║ CD

EF be the transversal passing through the two parallel lines at P and Q respectively.

PR and QS are the bisectors of ∠EPB and ∠PQD.

We know that the corresponding angles of parallel lines are equal,

So, ∠EPB = ∠PQD

½ ∠EPB = ½ ∠PQD

∠EPR = ∠PQS

But, we also know that they are corresponding angles of PR and QS

Since the corresponding angles are equal,

We have,

PR ║ QS

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.

Categories

...