M L Aggarwal Solutions for Chapter: Triangles, Exercise 1: Exercise 7.1

In the following figure, $AB=AC$, $P \text{and} Q$ are points on $BA$ and $CA$ respectively such that $AP=AQ$. Prove that $\angle ACP=\angle ABQ$.

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

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

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

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

In the following figure, $\angle BCD=\angle ADC$ and $\angle BCA=\angle ADB$. Prove that $∆ACD=∆BDC$.

In the following figure, $\angle BCD=\angle ADC$ and $\angle BCA=\angle ADB$. Prove that $BC=AD$.

In the following figure, $\angle BCD=\angle ADC$ and $\angle BCA=\angle ADB$. Prove that $\angle A=\angle B$.