Congruence of Triangles

In figure, $BC$ and $\overline{AD}$ intersect at $E$. 

Find $BA$ and $CD$

In the adjoining figure, $ABC$ is an isosceles triangle with $AB= AC$ and also given that $EC= BD$. Prove that $AE= AD$.

Use the congruency of triangles to find the value of $x$ and $y$ in following figure.

Use the congruency of triangles to find the value of $x$ and $y$ in following figure.

Given that $△ABC\cong △PQR$, so explain what it means and if side $BC=7$ units, then find the length of side $QR$.

Given that $△ABC\cong △PQR$, so explain what it means and if side $AC=5$ units, then find the length of side $PR$.

What are congruent Squares?

These shapes are congruent.

Which of the following figures are congruent to the square $ABCD$.

In figure $OA=OB$ and $OD=OC$. Show that $AD\parallel BC$.

In figure $OA=OB$ and $OD=OC$. Show that $△AOD\cong △BOC$.

Define the congruency of two triangles.

How can two squares have the same angles but not be congruent?

Two squares are congruent if both of them have the same length of the _____.

In the figure below, O is the centre of the circle. A and B are points on the circle. ∠OAP and ∠OBP are right angles.

Which of the following congruence rules can we use to prove PA = PB?

In the figure below, AE = DE and BE = CE.

Choose the suitable approach to prove that AB = CD.

From a point $\mathrm{P}$ outside a circle, with circle $\mathrm{O}$, tangent $\mathrm{PA}$ and $\mathrm{PB}$ are drawn. Prove that $\angle \mathrm{AOP}=\angle \mathrm{BOP}$.

Show that the circle drawn with any one of the equal sides of an isosceles triangle as diameter bisects the base of that isosceles triangle.
 

In the given figure,$\mathrm{AC}=\mathrm{AE}$. Show that: $\mathrm{BP}=\mathrm{DP}.$

In the given figure, $\mathrm{AC}=\mathrm{AE}$. Show that $\mathrm{CP}=\mathrm{EP}$.