M L Aggarwal Solutions for Chapter: Triangles, Exercise 3: Exercise 7.3

$ABC$ 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 $\angle BAC$.

 In the adjoining figure, $D$ and $E$ are points of $△ADC$ such that $BD=EC$ and $AD=AE$. Show that $△ABD\cong △ACE$.

In the figure given below, $CDE$ is an equilateral triangle formed on a side $CD$ of a square $ABCD$. Show that $∆ADE\cong ∆BCE$.

In the figure given below, $CDE$ is an equilateral triangle formed on a side $CD$ of a square $ABCD$. Show that $AEB$ is an isosceles triangle.

In the figure given below, $CDE$ is an equilateral triangle formed on a side $CD$ of a square $ABCD$. Show that  $\angle EAB=75°$.

In the figure given below, $O$ is a point in the interior of a square $ABCD$ such that $OAB$ is an equilateral triangle. Show that $OCD$ is an isosceles triangle.

 In the figure given below, bisectors of $\angle B$ and $\angle C$ of an isosceles triangle $ABC$ with  AB = AC intersect each other at O. BO is produced to a point M. Prove that $\angle MOC=\angle ABC$.

 In the figure given below, bisectors of $\angle B$ and $\angle C$ of an isosceles triangle $ABC$ with $AB=AC$ intersect each other at $O$. Show that the external angle adjacent to $\angle ABC$ is equal to $\angle BOC$.