$ABC$ is a right angled triangle in which $\angle A=90°$ and $AB=AC$. Find $\angle B$ and $\angle C$. 

$PQR$ is a triangle in which $PQ = PR$ and is any point on the side $PQ$. Through $S$, a line is drawn parallel to $QR$ and intersecting $PR$ at $T$. Prove that $PS = PT$.

In the figure given below $MN$ is parallel to $QR. PQ = PR$ and $LPN = 65°$. Find the measure of $\angle QPR$.

In the figure given below, $AB\parallel CD$. Find the values of $x, y$ and $z$.

In a triangle $ABC, AB=AC, D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $BD=CE$. Show that $△DBC\cong ∆ECB$.
 

In a triangle $ABC, AB=AC, D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $BD=CE$. Show that $\angle DCB=\angle EBC$.

In a triangle $ABC, AB=AC, D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $BD=CE$. Show that $OB=OC$ where $O$ is the point of intersection of $DE$ and $CD$.

$ABC$ is an isosceles triangle in which $AB=AC$. $P$ is any point in the interior of $∆ABC$ such that $\angle ABP=\angle ACP$ Prove that $BP=CP$.
 

$ABC$ is an isosceles triangle in which $AB=AC$. $P$ is any point in the interior of AADC such that $\angle ABP=\angle ACP$ Prove that $AP$ bisects $\angle BAC$.