Equilateral and Isosceles Triangle

In the figure $AB=AC$. Prove that $BD=BC$

In the given figure below$AN=AC$ , $\angle BAC=52°, \angle ACK=84°$ and $BCK$ is a straight line. Prove that $NB=NC$.

In $△ABC, \angle A=\angle B=50°$. Name the pair of sides which are equal.

In the following figure, $AD=BD, AE=EC$ and $m\angle AEB=100°$, $m\angle ABE=20°$. Find $m\angle CAB$.

The perpendicular drawn from the vertex to the opposite side bisects the base of isosceles and _____triangles.

The measure of each of the two opposite angles of a rhombus is $60°$ and the measure of one of its sides is $10 \mathrm{cm}$. The length of its smaller diagonal is

If $ABCD$ is a parallelogram, $△ADN$ and $△ABC$ are isosceles triangles, then find $\angle BAC$.