Q. 64.0( 17 Votes )

<span lang="EN-US

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.
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
RELATED QUESTIONS :

<span lang="EN-USMHB - Math Part-II

ΔABCMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II

<span lang="EN-USMHB - Math Part-II