Question

use the given information to prove that ( \triangle abccong\triangle adc ).
given: ( angle acb ) is a right angle
( angle acd ) is a right angle
( angle baccongangle dac )
prove: ( \triangle abccong\triangle adc )

Explanation:

Step1: Identify the property of \(\overline{AC}\)

\(\overline{AC}\) is common to both \(\triangle ABC\) and \(\triangle ADC\). So, \(\overline{AC}\cong\overline{AC}\) by the Reflexive Property of Congruence.

Step2: Determine the congruence of triangles

We have \(\angle ACB\cong\angle ACD\) (all right angles are congruent), \(\angle BAC\cong\angle DAC\) (given), and \(\overline{AC}\cong\overline{AC}\) (Reflexive Property). By the AAS (Angle - Angle - Side) Congruence Theorem, \(\triangle ABC\cong\triangle ADC\).

Answer:

1. Reason: Reflexive Property of Congruence
2. Reason: AAS (Angle - Angle - Side) Congruence Theorem