Chapter 4.8, Problem 45SPR

To determine

Two congruent angles.

Answer to Problem 45SPR

  $\angle \mathrm{T}\mathrm{S}\mathrm{R}\cong \angle \mathrm{T}\mathrm{R}\mathrm{S}$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The figure can be drawn as:

  

Two angles are marked by an arc, therefore,

  $\angle \mathrm{Q}\mathrm{R}\mathrm{S}\cong \angle \mathrm{Q}\mathrm{S}\mathrm{R}$

Two sides are marked with same slashes; hence, these two sides are equal.

  $\overline{\mathrm{R}\mathrm{T}}\cong \overline{\mathrm{S}\mathrm{T}}$

The angles inscribed by two equal sides with the third side of triangle are equal. Therefore,

  $\angle \mathrm{T}\mathrm{S}\mathrm{R}\cong \angle \mathrm{T}\mathrm{R}\mathrm{S}$