Question

partially correct
your answer is incorrect.

• statement 3: your answer is incorrect.
• statement 6: your answer is incorrect.

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 )
your answer

Explanation:

Step1: Correcting Statement 3

In statement 3, it should be \( \angle ACB=\angle ACD\) (since both are right - angles, and all right - angles are equal). The original \( \angle ACB = \angle ADC\) is wrong.

Step2: Verifying the Congruence Criterion

We have two angles (\( \angle BAC=\angle DAC\) and \( \angle ACB=\angle ACD\)) and the included side (\( \overline{AC}=\overline{AC}\) by reflexive property). The correct congruence criterion is ASA (Angle - Side - Angle) congruence property. The AAS (Angle - Angle - Side) is not the correct criterion here as the side is between the two angles.

Answer:

• Statement 3: \( \angle ACB=\angle ACD\) (Reason: All right angles are equal)
• Statement 6: \( \triangle ABC\cong\triangle ADC\) (Reason: ASA Congruence Property)