A K Upadhyay and S Upadhyay Solutions for Chapter: Congruent Triangles, Exercise 1: EXERCISE 7.1

In figure, $\angle Q=\angle R$, $PQ=PR$ and $QM$ and $RN$ intersects at $O.$ Prove that $PM=PN.$

In figure, $ABCD$ is a trapezium in which $AB\parallel CD$ and $F$ is the mid point of $AD$. On producing $BF$ meets $CD$ produced at $E.$Prove that: $CE=AB+CD.$

In figure, $ABCD$ is a square, $M$ is the mid point of $CD$ and $PQ\perp AM$ meets $AD$ at $P$ and $BC$ at $Q.$ Prove that $CQ=DP.$

In figure,$ABCD$ is a square, $M$  is the mid point of $CD$ and $PQ\perp AM$ meets $AD$ at $P$ and $BC$ at $Q.$ Prove that $AQ=CQ+CD$

In the given figure, $\angle BCD=\angle ADC$ and $\angle ACB=\angle BDA$. Prove that $\angle A=\angle B$

In figure $BA\parallel PQ, CA\parallel RS$ and $BP=RC.$ Prove that $RS=CQ.$

In figure, $\mathrm{O}\mathrm{A}\perp \mathrm{O}\mathrm{D}, \mathrm{O}\mathrm{C}\perp \mathrm{O}\mathrm{B}, \mathrm{O}\mathrm{D}=\mathrm{O}\mathrm{A}$ and $OC = OB$. Prove that $AB = CD.$

$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a rectangle $\mathrm{X}$ and $\mathrm{Y}$ are points on sides $\mathrm{A}\mathrm{D}$ and $\mathrm{B}\mathrm{C}$ respectively such that $\mathrm{C}\mathrm{X}=\mathrm{D}\mathrm{Y}$. Prove tha $\mathrm{C}\mathrm{Y}=\mathrm{D}\mathrm{X}$ and $\mathrm{\angle }\mathrm{C}\mathrm{D}\mathrm{Y}=\mathrm{\angle }\mathrm{D}\mathrm{C}\mathrm{X}$.