Chapter 4, Problem 15MCQ

To determine

The correct statement.

Answer to Problem 15MCQ

  $\angle \mathrm{C}\cong \angle \mathrm{S}$

Explanation of Solution

Given:

  $\mathrm{\Delta }\mathrm{C}\mathrm{B}\mathrm{X}\cong \mathrm{\Delta }\mathrm{S}\mathrm{M}\mathrm{L}$

Calculation:

According to corresponding parts of congruent triangles,

Angles:

  $\angle \mathrm{C}\cong \angle \mathrm{S},\angle \mathrm{B}\cong \angle \mathrm{M},\angle \mathrm{X}\cong \angle \mathrm{L}$

Sides:

  $\overline{\mathrm{C}\mathrm{B}}\cong \overline{\mathrm{S}\mathrm{M}},\overline{\mathrm{B}\mathrm{X}}\cong \overline{\mathrm{M}\mathrm{L}},\overline{\mathrm{X}\mathrm{C}}\cong \overline{\mathrm{L}\mathrm{S}}$

Hence,

  $\angle \mathrm{X}\mathrm{C}\mathrm{B}\cong \angle \mathrm{L}\mathrm{S}\mathrm{M}$

Because $\angle \mathrm{C}\cong \angle \mathrm{S}$