Criteria for Congruence of Triangles

If the above two isosceles triangles are congruent and if $\angle B=80°$, then find $\angle B_1$.

If the above two isosceles triangles are congruent and if $\angle B=110°$, then find $\angle B_1$.

If the above two isosceles triangles are congruent and if $\angle B=120°$, then find $\angle B_1$.

If the equal sides and the angle included between the equal sides of the triangles are equal to each other, then $\frac{AC}{DF}=1$.

If the equal sides and the angle included between the equal sides of the triangles are equal to each other, then prove that $AC=DF$.

If the equal sides and the angle included between the equal sides of the triangles are equal to each other, then prove that $\angle A=\angle D$.

Prove that any two isosceles triangles are congruent if the equal sides and the angle included between the equal sides of the triangles are equal to each other?

If their sides are equal to each other in the two right-angled isosceles triangles given, then $\angle A=\angle E$. 

In the two right-angled isosceles triangles, prove that $\angle B=\angle E$ if their sides (other than the hypotenuse) are equal to each other?

In the two right-angled isosceles triangles, prove that $AB=DE$ if their sides (other than the hypotenuse) are equal to each other?

Prove that any two right-angled isosceles triangles are congruent if their sides are equal to each other?

What is congruence among the right-angled isosceles triangles?

In the figure, line segments $AB$ and $CD$ bisect each other at $O$. Is $\Delta AOC\cong \Delta BOD$?

In the given pair of triangles, parts bearing identical marks are congruent. State the test by which triangles are congruent. $RHS/SSS/SAS/ASA$

In the given pair of triangles, parts bearing identical marks are congruent. State the corresponding vertex to $X$.

In Figure, $△$ $ABC$ is right angled at $B$. $ACDE$ and $BCGF$ are squares. Prove that $AG=BD$.

In Figure, $△$ $ABC$ is right angled at $B$. $ACDE$ and $BCGF$ are squares. Prove that   $△$$BCD$$\cong$$△$$ACG$

In Fig., $PQRS$ is a square and $LM$ is parallel to $PR$. $N$ is the mid point of $LM$. Prove that $QN$ on producingwill pass through $S$.

In Fig., $PQRS$ is a square and $LM$ is parallel to $PR$. $N$ is the mid point of $LM$. Prove that $QN$ bisects $\angle PQR$

In Fig., $PQRS$ is a square and $LM$ is parallel to $PR$. $N$ is the mid point of $LM$. Prove that $PL = RM$