Q. 35.0( 5 Votes )

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

Answer :


Given that perpendiculars from any point within an angle on its arms are congruent.


We have to prove that it lies on the bisector of that angle.


Now, let us consider an 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


We have,


BMP = BNP = 90o (Given)


BP = BP (Common)


MP = NP (Given)


So, by RHS congruence rule, we have



MBP = NBP (By c.p.c.t)


BP is the angular bisector of ABC


Hence, proved


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Mastering TrianglesChamp Quiz | Mastering TrianglesChamp Quiz | Mastering Triangles44 mins
RD Sharma | Important Proofs in TrianglesRD Sharma | Important Proofs in TrianglesRD Sharma | Important Proofs in Triangles28 mins
Triangles - Important QuestionsTriangles - Important QuestionsTriangles - Important Questions39 mins
Quiz | Are You Master of Triangles?Quiz | Are You Master of Triangles?Quiz | Are You Master of Triangles?48 mins
NCERT | Triangle InequalitiesNCERT | Triangle InequalitiesNCERT | Triangle Inequalities47 mins
NCERT | Practice Imp. Qs. on TrianglesNCERT | Practice Imp. Qs. on TrianglesNCERT | Practice Imp. Qs. on Triangles44 mins
R.D. Sharma | TrianglesR.D. Sharma | TrianglesR.D. Sharma | Triangles33 mins
Champ Quiz | Congruency of TrianglesChamp Quiz | Congruency of TrianglesChamp Quiz | Congruency of TrianglesFREE Class
Champ Quiz | Know About TrianglesChamp Quiz | Know About TrianglesChamp Quiz | Know About Triangles50 mins
Quiz on TrianglesQuiz on TrianglesQuiz on Triangles32 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses