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: Analyze the given triangles

We have \(\triangle ABC\) and \(\triangle ADC\). We know that \(BC = DC\) (common side), \(\angle B=\angle D\) (right angles), and \(\angle BAC=\angle DAC\) (given angles).

Step2: Recall the postulates

• \(ASA\) (Angle - Side - Angle): Two angles and the included side.
• \(SAS\) (Side - Angle - Side): Two sides and the included angle.
• \(AAS\) (Angle - Angle - Side): Two angles and a non - included side.
• \(SSS\) (Side - Side - Side): Three sides.

In \(\triangle ABC\) and \(\triangle ADC\), we have two angles (\(\angle B=\angle D\) and \(\angle BAC = \angle DAC\)) and a non - included side (\(AC = AC\) common side).

Answer:

C. \(AAS\) Postulate