Chapter 4, Problem 13PT

To determine

The postulate or theorem that can be used to prove each pair of triangles congruent.

Answer to Problem 13PT

  $\Delta BDA\cong \Delta BDC\text{ (AAA Congruence Theorem)}\text{.}$

Explanation of Solution

Given:

The given figure is:

  

Calculation:

If the 2 angles and the non-included side of one triangle is congruent to the 2 angles and non-included side of another triangle, then the two triangles are congruent.

Label the diagram given:

  

Angle A is congruent to angle C and angle BDA is congruent to angle CDA.

According to the reflexive property of congruence, line BD is congruent to BD.

Therefore,

  $\Delta BDA\cong \Delta BDC\text{ (AAA Congruence Theorem)}\text{.}$