# 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.

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by chiragsa

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by chiragsa

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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.

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 .