Congruence of T...

$$\Delta ABC$$ is congruent of $$\Delta DEF$$, if

If $$D$$ and $$E$$ are the mid-points of the sides $$AB$$ and $$AC$$ respectively of $$\triangle ABC$$. $$DE$$ is produced to $$F$$. To prove that $$CF$$ is equal and parallel to $$DA$$, we need an additional information which is:

In $$\triangle ABC$$ and $$\triangle DEF$$, $$AB = FD$$ and $$\angle A = \angle D.$$ The two triangles will be congruent by $$SAS$$ axiom, if:

By which congruency are the following pair of triangles congruent:

In $$\Delta\,ABC$$ and $$\Delta \,DEF$$, $$\angle\,B = \angle\,E = 90\,^{\circ}, AC = DF$$ and $$BC = EF.$$

In the figure $$\angle  ABC=135^{\circ},\angle ABX=90^{\circ} ,\angle XCD=55^{\circ}, \angle BCD=100^{\circ}$$,then determine whether $$\angle XBC$$ and $$\angle XCB$$ are congruent to each other.

Which pair of triangles is not congruent by $$SAS$$ congruence criterion 

If $$AB=QR$$, $$BC=PQ$$ and $$CA=PR$$, then:

$$l$$ and $$m$$ are two parallel lines intersected by another pair of parallel lines $$p$$ and $$q$$. Then:

State the property by which $$\Delta ADB\, \cong\, \Delta ADC$$ in the following figure.,

If in two triangles $$PQR$$ and $$DEF$$, $$PR=\,EF$$, $$QR=\,DE$$ and $$PQ=\,FD$$, then  $$\triangle PQR\cong$$ $$\triangle$$ ___.