Question

Can you deduce from the given information that $△\mathbf{RXY}\cong △\mathbf{SXY}$? If so, what postulate can you use?

Given:$\angle \mathbf{RXY}\cong \angle \mathbf{SXY}$ ; $\overline{\mathrm{RX}}\cong \overline{\mathrm{SX}}$.

Short answer

Yes, it can be deduced from the given information that$△RXY\cong △SXY$.

The postulate that can be used is SAS postulate.

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Description of step.

It is being given that$\angle RXY\cong \angle SXY$ and $\overline{RX}\cong \overline{SX}$.

In the triangles$△RXY$ and $△SXY$, the side that is common is$XY$ .

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

In the triangles $△RXY$ and$△SXY$ , it can be noticed that$\overline{RX}\cong \overline{SX}$, and$\angle RXY\cong \angle SXY$.

Therefore, the triangles $△RXY$and $△SXY$are the congruent triangles by using the SAS postulate.

- Write the conclusion.

Yes, it can be deduced from the given information that$△RXY\cong △SXY$.

The postulate that can be used is SAS postulate.