Prove that the bisectors of the base angles of an isosceles triangle are equal.

In the figure alongside, $AB=AC, \angle A=48°$ and $\angle ACD=18°$. Show that $BC=CD$

Use the given figure to prove that, $AB = AC$.

In the given figure; $AE$ bisects exterior angle $CAD$ and $AE$ is parallel to $BC$. Prove that: $AB=AC$.

From the following figure, prove that :

$\angle ACD = \angle CBE$

From the following figure, prove that :

$AD=CE$

In the following figure; $IA$ and $IB$ are bisectors of angles $CAB$ and $CBA$ respectively. $CP$ is parallel to $IA$ and $CQ$ is parallel to $IB$.

Prove that:

$PQ =$ The perimeter of the $△ABC$.

Sides $AB \text{and} AC$ of a triangle $ABC$ are equal. $BC$ is produced through $C$ up to point $D$ such that $AC = CD$. $D$ and $A$ are joined and produced (through vertex $A$) up to point $E$. If angle $BAE=108°$; find angle $ADB$.

Using the information, given in each of the following figures, find the values of $a \text{and} b$.

$\left[\text{Given}: CE=AC\right]$