Question

6 which of the following can be used to prove that (\triangle abccong\triangle adc)?
a (asa) postulate
b (sas) postulate
c (aas) postulate
d (sss) postulate

Explanation:

Step1: Identify the given information

We have two triangles \(\triangle ABC\) and \(\triangle ADC\). We know that \(\angle B=\angle D\) (right - angles or given equal angles in the figure), \(AC = AC\) (common side, so \(AC\) is congruent to itself by the reflexive property of congruence: \(AC\cong AC\)), and \(\angle BAC=\angle DAC\) (given by the angle markings in the figure).

Step2: Recall the congruence postulates

• ASA (Angle - Side - Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
• AAS (Angle - Angle - Side): If two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
• SSS (Side - Side - Side): If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

In our case, we have two angles (\(\angle B=\angle D\) and \(\angle BAC = \angle DAC\)) and a non - included side (\(AC\)) that are congruent.

Answer:

C. \(AAS\) Postulate