Question

Construct an isosceles triangle, given its base and base angle justify the construction.

Answer 1

Let $△ABC$ be the isosceles triangle where,

$BC=AC$

$\Rightarrow \angle A=\angle B[\because$ Angles opposite to equal sides are equal $]$

Let,

$AB=x$ cm and $\angle A=\angle B=\theta$

Steps for construction :

Step 1: Draw the base $AB$.

Step 2: Construct $\angle XAB=\theta$ at point $A$.

Step 3: Similarly construct $\angle YBA=\theta$ at point $B$.

Step 4: Mark the intersecting point of ray $AX$ and $BY$ as point $C$.

Hence, the required $△ABC$ is constructed.