Chapter 4.3, Problem 8CYU

To determine

To prove:

  $\mathrm{\Delta }\mathrm{W}\mathrm{X}\mathrm{Z}\cong \mathrm{\Delta }\mathrm{Y}\mathrm{X}\mathrm{Z}$ in the form of paragraph proof .

Explanation of Solution

Given information:

  

  $\begin{array}{l}\angle \mathrm{W}\mathrm{X}\mathrm{Z}\cong \angle \mathrm{Y}\mathrm{X}\mathrm{Z}\\ \angle \mathrm{X}\mathrm{Z}\mathrm{W}\cong \angle \mathrm{X}\mathrm{Z}\mathrm{Y}\\ \overline{\mathrm{W}\mathrm{X}}\cong \overline{\mathrm{Y}\mathrm{X}}\\ \overline{\mathrm{W}\mathrm{Z}}\cong \overline{\mathrm{Y}\mathrm{Z}}\end{array}$

Proof:

Here, the given that $\overline{\mathrm{W}\mathrm{X}}\cong \overline{\mathrm{Y}\mathrm{X}},\overline{\mathrm{W}\mathrm{Z}}\cong \overline{\mathrm{Y}\mathrm{Z}}$ and $\overline{\mathrm{X}\mathrm{Z}}\cong \overline{\mathrm{X}\mathrm{Z}}$ by the reflexive property. It is also given that $\angle \mathrm{W}\mathrm{X}\mathrm{Z}\cong \angle \mathrm{Y}\mathrm{X}\mathrm{Z},\angle \mathrm{X}\mathrm{Z}\mathrm{W}\cong \angle \mathrm{X}\mathrm{Z}\mathrm{Y}$ and by the third angles theorem $\angle \mathrm{W}\cong \angle \mathrm{Y}$ . Therefore by the definition of congruent polygons get that $\mathrm{\Delta }\mathrm{W}\mathrm{X}\mathrm{Z}\cong \mathrm{\Delta }\mathrm{Y}\mathrm{X}\mathrm{Z}$ .