Question

State true or false:

In isosceles triangle $ABC$, sides $AB$ and $AC$ are equal. If midpoint $D$ lies in base $BC$ and point $E$ lies on $BC$ produced (BC being produced through vertex C), then $AC>AD$

If true enter 1 else 0

Answer 1

Let $ABC$ be the triangle and $BC$ be its base.

Let $AD$ be the line joining point $A$ to base $BC$.

Given $△ABC$ is isosceles, hence line joining the vertex to midpoint of its base is ${90}^o$

Here $△ABD$ and $△ADC$ are right angled triangles and $AB$ & $AC$

are the hypotenuses of $△ABD$ and $△ADC$ respectively.

Since a hypotenuse is greater than any of the sides of triangle,

$AB>AD$ and also $AC>AD$.