M L Aggarwal Solutions for Exercise 1: EXERCISE 10.1

In the adjoining figure, $ABCD$ is a quadrilateral in which $AD=BC$ and $\angle DAB=\angle CBA$. Prove that, $△ABD\cong △BAC$, $BD=AC$ and $\angle ABD=\angle BAC$.

In the adjoining figure, $AB=DC$ and $AB\parallel DC$. Prove that, $AD=BC$.

In the adjoining figure, $AC =AE, AB=AD$ and$\angle BAD=\angle CAE$. Show that, $BC=DE$.

In the adjoining figure, $AB=CD, CE=BF$ and $\angle ACE=\angle DBF.$ Prove that, $△ACE\cong △DBF$ and $AE=DF$.

In the adjoining figure, $AB=AC$ and $D$ is mid-point of $BC$. Use $SSS$ rule of congruency to show that $∆ABD\cong ∆ACD$.

In the adjoining figure, $AB=AC$ and $D$ is mid-point of $BC$. Show that $AD$ is bisector of $\angle A$.

In the adjoining figure, $AB=AC$ and $D$ is mid-point of $BC$. Show that $AD$ is perpendicular to $BC$.

In the adjoining figure, find the values of $x$ and $y$.