Question

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

Given:$\overline{\mathrm{RX}}\cong \overline{\mathrm{SX}}$; $\overline{\mathrm{RY}}\cong \overline{\mathrm{SY}}$

Short answer

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

The postulate that can be used is SSS postulate.

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Description of step.

It is being given that$\overline{RX}\cong \overline{SX}$and$\overline{RY}\cong \overline{SY}$.

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

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

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

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

- Write the conclusion.

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

The postulate that can be used is SSS postulate.