Question

the two triangles shown in the diagram share a side.
which criterion for triangle congruence will determine the congruence of the two triangles?
○ angle-side-angle
○ angle-angle-side
○ side-side-angle
○ side-side-side

Explanation:

Step1: Analyze the given information

We know that the two triangles share a common side. Also, from the markings on the diagram, the other two pairs of sides are equal.

Step2: Recall the triangle congruence criteria

• Angle - Side - Angle (ASA): Requires two angles and the included side to be equal.
• Angle - Angle - Side (AAS): Requires two angles and a non - included side to be equal.
• Side - Side - Angle (SSA): Is not a valid congruence criterion in general (except for right - angled triangles as Hypotenuse - Leg).
• Side - Side - Side (SSS): Requires all three pairs of sides to be equal.

Since we have three pairs of equal sides (the two marked pairs and the common side), the SSS criterion is applicable.

Answer:

Side - Side - Side