Question

1. which theorem would be used to prove the triangles below as congruent?

aaa
sss
sas
hl

Explanation:

The image shows two triangles, △SRT and △URT. The segments SR and UR are marked congruent (red crosses), the angles at R (∠SRT and ∠URT) are marked congruent (red arcs), and the side RT is common to both triangles. This matches the SAS (Side-Angle-Side) congruence theorem, where two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle.

The triangles share side RT. Segments SR ≅ UR (marked), angles ∠SRT ≅ ∠URT (marked). This is two sides and the included angle congruent, matching SAS.

Answer:

SAS (assuming the option is labeled correctly; based on the markings, SAS is the correct theorem)

Wait, correcting to follow multiple-choice format properly: Since the options are AAA, SSS, SAS, HL, the correct option is SAS.