Chapter 4, Problem 7CR

To determine

To describe: whether the given condition 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:

  

The line segment $\overline{XY}$ bisects $\angle RXS$ and $\angle RYS.$

Concept used:

• The bisector is a line that divides the angle in to two equal angles.

• ASA postulate:

When two angles and included side of one triangle are congruent to two angles and the included side of the other triangle, then the triangles are congruent by ASA postulate.

From the definition of angle bisector,

  $\angle RXY=\angle YXS$

  $\angle RYX=\angle XYS$

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

As the two angles and included side of triangle RXY are congruent to the two angles and included side of the triangle SXY, so, using ASA postulate, $\Delta RXY\cong \Delta SXY$ .

Hence, the given condition is deduced from ASA postulate.