Question

In figure, AD = DC and AB = BC

(a) Is $\Delta ABD\cong \Delta CBD?$

(b) State the three parts of matching pairs you have used to answer (a).

Answer 1

(a)Yes $\Delta ABD\cong \Delta CBD$ by the SSS criterion.

In SSS criterion, two triangles are congruent if the three sides of triangle are respectively equal to the three sides of the other triangle.

Hence $\Delta ABD\cong \Delta CBD$

(b) We have used the three conditions in the SSS criterion as follows:
AD = DC
AB = BC and
DB = BD