Question

multiple choice 1 point
determine if the triangles can be proved congruent, if possible, by sss, sas, asa, aas, or hl.
image of triangles with markings
options:

• not congruent
• sss congruence
• asa congruence
• hl congruence
• aas congruence
• sas congruence (selected)

Explanation:

Step1: Identify Given Information

In triangles \( \triangle SUV \) and \( \triangle T UW \):

• \( SU = TU \) (marked with one tick mark on \( ST \), so \( SU = TU \)).
• \( \angle SUV = \angle TUW \) (vertical angles, so they are equal).
• \( SV = TW \) (marked with one tick mark on \( SV \) and \( TW \)).

Step2: Apply SAS Congruence Criterion

The SAS (Side - Angle - Side) congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Here, we have two sides (\( SU = TU \) and \( SV = TW \)) and the included angle (\( \angle SUV=\angle TUW \)) congruent between \( \triangle SUV \) and \( \triangle TUW \). So, by SAS congruence, the triangles are congruent.

Answer:

SAS Congruence