Sarthaks Test
0 votes
in Mathematics by (7.9k points)

If perpendiculars from any point within an angle on its arms are congruent, prove that it lies on the bisector of that angle.

1 Answer

+1 vote
by (13.1k points)
selected by
Best answer

Given that, if perpendicular from any point within, an angle on its arms is congruent, prove that it lies on the bisector of that angle


Let us consider an angle ABC and let BP be one of the arm within the angle

Draw perpendicular PN and PM on the arms BC and BA such that they meet BC and BA in N and M respectively.

Now, in ΔBPM and ΔBPN

We have

∠BMP =∠BNP = 90°  [given]

BP = BP   [Common side]

And MP = NP  [given]

So, by RHS congruence criterion, we have



∠MBP =∠NBP   [ ∵ Corresponding parts of congruent triangles are equal]

⇒ BP is the angular bisector of ∠ABC.

∴ Hence proved

by (10 points)
there is much to be written

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.