Chapter 4, Problem 14PT

To determine

The postulate or theorem that can be used to prove the triangles congruent.

Answer to Problem 14PT

  $\mathrm{\Delta }\mathrm{A}\mathrm{B}\mathrm{C}\cong \mathrm{\Delta }\mathrm{C}\mathrm{D}\mathrm{A}$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

It is given that,

  $\begin{array}{l}\overline{\mathrm{A}\mathrm{B}}\cong \overline{\mathrm{C}\mathrm{D}}\\ \overline{\mathrm{B}\mathrm{C}}\cong \overline{\mathrm{D}\mathrm{A}}\end{array}$

According to the reflexive property,

  $\overline{\mathrm{A}\mathrm{C}}\cong \overline{\mathrm{C}\mathrm{A}}$

Therefore, by SSS postulate,

  $\mathrm{\Delta }\mathrm{A}\mathrm{B}\mathrm{C}\cong \mathrm{\Delta }\mathrm{C}\mathrm{D}\mathrm{A}$