Criteria for Congruence of Triangles

Which of the following pair of triangles are congruent by RHS criterion?

Tiara wants to know the width of the given river. While doing so, she stands on the edge of the river and look straight across to a point on the other edge without changing the inclination of the neck and head. She turns sideways until the vision is in line with a point on the side of the stream.

From the above description, find the value of $\mathrm{QR}$.

Akira gave a problem to her sister Kiara. However, Kiara got stuck. Help Kiara identify whether the triangles are congruent and choose the correct option.

Ananya is designing the window shown in the figure. She wants to make $∆PRQ$ congruent to $∆PRS$. She designs the window so that $PR\perp QS$. Which of the following conditions will make the two triangles congruent?

In two triangles $\mathrm{PQR}$ and $\mathrm{LMN}$, $\mathrm{PQ}=\mathrm{QR},\mathrm{\angle }\mathrm{P}=\mathrm{\angle }\mathrm{M}$ and $\mathrm{QR}=\mathrm{LN}$, then which of the following statements is CORRECT?

By which congruency criterion, $∆\mathrm{PQR}\cong ∆\mathrm{PQS}$?

If for $∆ABC$ and $∆DEF$, the correspondence $CAB\leftrightarrow EDF$ gives a congruence, then which of the following is not true?

$∆\mathrm{PQR}\cong ∆\mathrm{XYZ}$ by _____ congruence rule.
 

Study the figure and information given below carefully and answer the following questions.

$CF$ and $AE$ are equal perpendiculars on $BD$ and $BF=FE=ED$.

$\angle$ $BAE=$_____.

If $∆\mathrm{ABC}\cong ∆\mathrm{PRQ}$, then $\angle \mathrm{B}$ and $\mathrm{PQ}$ are respectively equal to