Chapter 4, Problem 8CR

To determine

To describe: whether the condition $\Delta RXY\cong \Delta SXY$ is deduced from the given

information or not and to give the name of the postulate used.

Explanation of Solution

Given information:

The given figure is as follows:

  

  $\angle RXY\cong \angle SXY$ and $\overline{RX}\cong \overline{SX}$ .

Concept used:

• SAS postulate:

When two sides and included angle of one triangle are congruent to the two sides and included angle of the other triangle, then two triangles are said to be congruent by SAS postulate.

Consider the two triangles $\Delta RXY$ and $\Delta SXY$

(i) $\overline{RX}\cong \overline{SX}$ (Given)

(ii) $\angle RXY\cong \angle SXY$ (Given)

(iii) $\overline{XY}=\overline{XY}$ (Common side)

As in $\Delta RXY$ and $\Delta SXY$ two corresponding sides and included angle are congruent, so, by using SAS postulate, $\Delta RXY\cong \Delta SXY$ .

Hence, the given condition is deduced from SAS postulate.