Question

ABC is an isosceles triangle in which AB = AC. M is the mid-point of AB and MN||BC. Show that ΔAMN is also an isosceles triangle.

Answer 1

Given : ABC is an isosceles triangle.
             AB = AC And M is the mid point of AB
              MN || BC
To prove : ΔAMN is an isosceles triangle
                    or
                 AM = AN

Proof : Since M is the mid point of AB and MN || BC
           ∴ N is the mid point of AC( By converse of mid point theorem.)
           
In Δ ABC
AB = AC
1/2 AB = 1/2AC
AM = AN ( N is the mid point of  AC)

∴ ΔAMN is an isosceles triangle.

Answer 2

To prove - ∆AMN is an isosceles triangle .


Proof - In ∆ABC ,
M is the mid point of AB and MN // BC
=> N is also the mid point of AC (BY Mid point Theorem)
*AB = AC (Given)
1/2AB = 1/2AC
=>AM = AN
Therefore , ∆AMN is an isosceles triangle .