If the bisector o

Given in Δ ABC, AD bisects the A meeting BC at D

Construction:- Extend BA to E and join C to E such CE AD……… 4

BAD = AEC (corresponding s)……………… 2

CAD = ACE (alternate interior s)……………….. 3

From 1 , 2 and 3

ACE = AEC

In Δ AEC

ACE = AEC

AC = AE (sides opposite to equal angles are equal)……….. 5

In Δ BEC

And D is midpoint of BC (given)

By converse of midpoint theorem

A line drawn from the midpoint of a side, parallel to the opposite side of the triangle meets the third side in its middle and is half of it

A is midpoint of BE

BA = AE……… 6

From 5 and 6

AB = BC

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
view all courses
RELATED QUESTIONS :

<img width=RD Sharma - Mathematics

<img width=RD Sharma - Mathematics

If <img widRD Sharma - Mathematics

The areas of two RD Sharma - Mathematics

The areas of two RD Sharma - Mathematics

In Fig. 4.236, <sRD Sharma - Mathematics

If <img widRD Sharma - Mathematics

If the altitude oRD Sharma - Mathematics

If the areas of tRD Sharma - Mathematics