Chapter 4, Problem 16PT

To determine

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

Answer to Problem 16PT

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

Explanation of Solution

Given:

The given figure is:

  

Calculation:

The figure can be drawn as:

  

It is given that,

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

According to the reflexive property,

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

Therefore, by SAS postulate,

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