Question

select the correct answer. which criterion can be used to prove abc and adc are congruent? a. sss b. aaa c. sas d. asa

Explanation:

Step1: Analyze the given information

We have two triangles \(ABC\) and \(ADC\). From the figure, we can observe that \(AC = AC\) (common side). Also, we can assume that \(AB = AD\) (if we consider the markings of equal lengths from the figure's structure) and \(\angle BAC=\angle DAC\) (given as equal angles).

Step2: Recall the congruence criteria

• SSS (Side - Side - Side): Requires three pairs of equal sides. We only know one pair of common sides here initially (without more information about all three sides).
• AAA (Angle - Angle - Angle): Only gives similarity, not congruence.
• SAS (Side - Angle - Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. Here, if \(AB = AD\), \(\angle BAC=\angle DAC\), and \(AC = AC\) (side - angle - side).
• ASA (Angle - Side - Angle): Requires two angles and the included side. We don't have information about two angles and the included side in the given problem description (based on the visual cues of equal sides and one pair of equal angles)

Answer:

C. SAS