Question

In the following pairs of triangles (Fig. 12 to 15), the lengths of the sides are indicated along sides. By applying SSS condition, determine which are congruent. State the result in symbolic form.

Answer 1

1) In $∆\text{ABC and ∆DEF}$
AB = DE = 4.5 cm (Side)
BC = EF = 6 cm (Side)
and AC = DF = 4 cm (Side)

Therefore, by SSS criterion of congruence, $△\text{ABC}\cong △\text{DEF}$.

2)
$$\begin{gathered} \text{In}△\text{ACB and}△\text{ADB} \\ \text{AC =AD (Side)} \\ \text{BC = BD (Side)} \\ \text{and AB\hspace{0.17em}=AB (Side)} \end{gathered}$$
Therefore, by SSS criterion of congruence, ​$△\text{ACB}\cong △\text{ADB}$.

3)
$$\begin{gathered} \text{In}△\text{ABD and}△\text{FEC,} \\ \text{AB = FE (Side)} \\ \text{AD = FC (Side)} \\ \text{BD = CE (Side)} \end{gathered}$$
Therefore, by SSS criterion of congruence, $△\text{ABD}\cong △\text{FEC}$.