Question

For each diagram, name a pair of overlapping triangles. Tell whether the triangles are congruent by the $\mathit{S}\mathit{S}\mathit{S}\mathbf{,}\mathbf{}\mathit{S}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathit{A}\mathit{S}\mathit{A}\mathbf{,}\mathbf{}\mathit{A}\mathit{A}\mathit{S}\mathbf{,}\mathbf{}\mathbf{\text{or}}\mathbf{}\mathit{H}\mathit{L}$method.

10. Given: $\overline{\mathrm{AB}}\mathbf{\cong }\overline{\mathrm{DC}}\mathbf{;}\mathbf{}\overline{\mathrm{AC}}\mathbf{\cong }\overline{\mathrm{DB}}$

Short answer

The pair of overlapping triangles that are congruent are$△\mathbf{ABC}$and $△\mathbf{DCB}$.

The triangles$△ABC$ and$△DCB$ are congruent by the SSS method.

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Description of step.

It is being given that$\overline{AB}\cong \overline{DC}$and $\overline{AC}\cong \overline{DB}$.

In the triangles$△ABC$ and $△DCB$, the side that is common is $BC$.

Therefore,$\overline{BC}\cong \overline{BC}$by using the reflexive property.

In the triangles $△ABC$ and $△DCB$, it can be noticed that$\overline{AB}\cong \overline{DC},\overline{BC}\cong \overline{BC}$ and$\overline{AC}\cong \overline{DB}$.

Therefore, the triangles $△ABC$and $△DCB$are the congruent triangles by using the $SSS$method.

- Write the conclusion.

The pair of overlapping triangles that are congruent are$△ABC$ and $△DCB$.

The triangles$△ABC$ and$△DCB$ are congruent by the SSS method.