Question : If m$\angle$C = m$\angle$Z and AC = XZ, which of the following conditions is necessary for ΔABC and ΔXYZ to be congruent?

Question : In an isosceles $\triangle ABC$, $AB = AC$, $XY || BC$. If $\angle A=30°$, then $\angle BXY$?

Question : $\Delta ABC$ and $\Delta DEF$ are two similar triangles and the perimeters of $\Delta ABC$ and $\Delta DEF$ are 90 cm and 54 cm respectively. If the length of DE = 36 cm, then the length of AB is: 

Question : In $\triangle$ABC, $\angle$B = 35°, $\angle$C = 65° and the bisector of $\angle$BAC meets BC in D. Then $\angle$ADB is:

Question : In $\triangle$ABC and $\triangle$DEF, $\angle$A = $55^{\circ}$, AB = DE, AC = DF, $\angle$E = $85^{\circ}$ and $\angle$F = $40^{\circ}$. By which property are $\triangle$ABC and $\triangle$DEF congruent?