R K Bansal Solutions for Exercise 1: EXERCISE

In the following figure, $\angle A=\angle C$ and $AB=BC$. Prove that $△ABD\cong △CBE$.

$AD$ and $BC$ are equal perpendiculars to a line segment $AB$. If $AD$ and $BC$ are on different sides of $AB$, prove that $CD$ bisects $AB$.

In $△ABC, AB=AC$ and the bisectors of angles $B$ and $C$ intersect at point $O$. Prove that $BO=CO$.

In $△ABC, AB=AC$ and the bisectors of angles $B$ and $C$ intersect at point $O$. Prove that $AO$ bisects angle $BAC$.

In the following figure, $AB=EF, BC=DE$ and $\angle B=\angle E=90°$. Prove that $AD=FC$.

A point $O$ is taken inside a rhombus $ABCD$ such that its distances from the vertices $B$ and $D$ are equal. Show that $AOC$ is a straight line.

In a quadrilateral $ABCD$, $AD=BC$ and $BD=CA$. Prove that $\angle ADB=\angle BCA$.

In a quadrilateral $ABCD$, $AD=BC$ and $BD=CA$. Prove that $\angle DAB=\angle CBA$.