Chapter 4.6, Problem 56SPR

To determine

Whether triangle ADC is congruent to triangle ABC.

Answer to Problem 56SPR

  $\Delta ADC\cong \Delta ABC.$

Explanation of Solution

Given:

The given figure is:

  

  $m\angle ADC=35,m\angle ABC=35,m\angle DAC=26,m\angle BAC=26$

Calculation:

According to the AAS Congruence Postulate, if 2 angles and a non-included side of first triangle are congruent to the corresponding 2 angles and the non-included side, then both the triangles are congruent.

From the given information;

  $m\angle ADC=m\angle ABC,m\angle DAC=m\angle BAC.$

According to the definition of congruence;

  $\angle ADC\cong \angle ABC\text{ and }\angle DAC\cong \angle BAC.$

According to the reflexive property of congruence;

  $\overline{AC}\cong \overline{AC}.$

Hence, $\Delta ADC\cong \Delta ABC.$