Question

2
5) prove that angles opposite to equal sides of a triangle are equal

D and E are point on side BC of tri ABC such that BD= CE and AD=AE.prove that AB=AC​

Answer 1

Step-by-step explanation:

1) Let us take an example of isosceles triangle ABC

with AB=AC

Now we have to prove angleB=angleC

draw an angle bisector of angle A which meets BC at D.

As we know that the angle bisector of intersection of equal sides in isosceles triangle is also a median and altitude of the isosceles triangle

So, We have

AB=AC (Given)

angleADB=angleADC (AD is altitude)

DB=DC (AD is median)

So as both the triangles are congruent by ASA, so

angleB=angleC

2) BD=CE (Given)

AD=AE (Given)

Adding both we get

AD+BD=AE+CE

As D is a point on AB and E is a point on AC ,

so

AB=AC