Question

Draw $\Delta CAR$ in which $CA=8cm$, $\angle A={60}^{\circ }$ and $AR=8cm$. Measure angle $C$. What kind of triangle is this ?

Answer 1

Steps of construction:

1. Draw a line segment $AB=8cm$

2. Draw a ray make angle ${60}^{\circ }$ at the centre $A$.

3. Draw an arc with radius $8cm$ on the ray, which intersects the ray at $C$.

4. Join $RC$.

Hence, required triangle $CAR$ formed.

As $AC=AR$ hence

$\angle C=\angle R=\theta$(say)

then ${60}^o+\theta +\theta ={180}^{\circ }$

$\therefore 2\theta ={120}^{\circ }$ or $\theta ={60}^{\circ }$

Hence, it is a equilateral triangle.