Question

question #10 g.gsr.3.4 which of the following pairs of triangles is congruent by the asa congruency theorem?

Explanation:

Step1: Recall ASA criterion

The ASA congruency theorem states that 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.

Step2: Examine option a

No clear indication of two angles and included - side equality.

Step3: Examine option b

No clear indication of two angles and included - side equality.

Step4: Examine option c

Two angles are marked equal and the side between them is common, satisfying ASA.

Step5: Examine option d

No clear indication of two angles and included - side equality.

Answer:

We need to analyze each option to see if it meets the ASA (Angle - Side - Angle) congruency criterion.

• Option a: There is not enough information to show two pairs of corresponding angles and the included side are equal.
• Option b: There is not enough information to show two pairs of corresponding angles and the included side are equal.
• Option c: In this pair of triangles, we can see two pairs of corresponding angles are marked as equal and the side between them is common (and thus equal), which satisfies the ASA congruency criterion.
• Option d: There is not enough information to show two pairs of corresponding angles and the included side are equal.

So the answer is c.