Question

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

Given:$\overline{\mathrm{RY}}\cong \overline{\mathrm{SY}}$;$\angle \mathbf{R}\cong \angle \mathbf{S}$

Short answer

No, it cannot be deduced from the given information that$△RXY\cong △SXY$.

Step-by-step solution

- Observe the given diagram.

The given diagram is:

- Description of step.

It is being given that$\overline{RY}\cong \overline{SY}$ and$\angle R\cong \angle S$.

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$\angle R\cong \angle S$,$\overline{XY}\cong \overline{XY}$ and$\overline{RY}\cong \overline{SY}$.

Therefore, it can be noticed that the triangles $△RXY$ and $△SXY$cannot be proved congruent by using any of the postulates.

Therefore, it cannot be deduced that the triangles $△RXY$ and $△SXY$are congruent triangles.

- Write the conclusion.

No, it cannot be deduced from the given information that $△RXY\cong △SXY$.