Q. 64.0( 17 Votes )

Prove that, if the bisector of BAC of ΔABC is perpendicular to side BC, then ΔABC is an isosceles triangle.

Answer :

Given: Bisector of BAC of ΔABC is perpendicular to side BC



To Prove: ΔABC is an isosceles triangle.


Proof:


In ΔABD and ΔACD


Since, AD is the angle Bisector of ΔABC


BAD = CAD


AD = AD ……….[Common Side]


ADB = ADC ……[Both equal to 90°]


So, by ASA congruency test


ΔABD ΔACD


Therefore,


AB = AC ………………. corresponding sides of congruent triangles.


ABD = ACD ……………… corresponding angles of congruent triangles.


ABC = ACB


Since, AB = AC and ABC = ACB so, ΔABC is an isosceles triangle.


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
R.D. Sharma | TrianglesR.D. Sharma | TrianglesR.D. Sharma | Triangles33 mins
NCERT | Most Important Questions of TrianglesNCERT | Most Important Questions of TrianglesNCERT | Most Important Questions of Triangles50 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
Triangles - Important QuestionsTriangles - Important QuestionsTriangles - Important Questions39 mins
RD Sharma | Problems on TrianglesRD Sharma | Problems on TrianglesRD Sharma | Problems on Triangles41 mins
Quiz | Are You Master of Triangles?Quiz | Are You Master of Triangles?Quiz | Are You Master of Triangles?48 mins
NCERT | Tricks to Apply Triangle InequalitiesNCERT | Tricks to Apply Triangle InequalitiesNCERT | Tricks to Apply Triangle Inequalities45 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