RHS and SSS Criteria for Congruence

In the given figure, $\mathrm{ABC}$ is a triangle with $\mathrm{BD}$ and $\mathrm{CE}$ perpendiculars to $\mathrm{AC}$ and $\mathrm{AB}$ respectively, such that $\mathrm{BD}=\mathrm{CE}$. Prove that $∆\mathrm{BCD}\cong ∆\mathrm{CBE}$.

​

$PQRS$ is a square whose diagonal $PR$ is joined. Prove that $△PQR\cong △PSR$.

In the figure,$\angle \mathrm{TEN}\equiv \angle \mathrm{TON}=90°$ and $\mathrm{TO}\equiv \mathrm{TE}.$ Prove that $\angle \mathrm{ORN}\equiv \angle \mathrm{ERN}$.

In the given figure, $D$ is the midpoint of $BC, DE\perp AB$ and $DF\perp AC$ such that $DE=DF$. Then, which of the following is true?

If in $∆ABC,AB=AC$ (see figure); $BP$ and $CQ$ be the altitudes from the vertices to their opposite sides, then

Which of the following is a correct statement?

In $△ABC$ if $AB = AC$ and $BD = DC$ see figure), then $\angle ADC =$

In the given figure,$x$ and $y$ are

In $∆PQR$, $\angle R=\angle P$ and $QR=4 \mathrm{cm}$ and $PR=5 \mathrm{cm}$. Then find the value of length of $PQ\times QR\times PR$.

In $∆ABC$, if $AB=AC$ and $\angle B=70°$, then $\angle C=2a°$. Find the value of $a$.

How many criterion of congruency of triangles are there?

The vertical angle of an isosceles triangle is $110°$. What is value of product of the digits in the measure of one of the equal angles?

In the figure, $BL\perp AC$, $MC\perp LN$, $AL=CN$ and $BL=CM$. Prove that $∆ABC\cong ∆NML$.