Question

1. are the below triangles congruent?

yes by sss
yes by sas
yes by asa
yes by aas
no

Explanation:

Step1: Identify marked angles

First triangle: 2 single-marked angles, 1 double-marked angle.
Second triangle: 2 single-marked angles, 1 double-marked angle.

Step2: Match congruence criterion

The unmarked side (between two angles in each triangle) is the side not directly marked, but we have two pairs of congruent angles and the non-included side that corresponds. This fits the AAS (Angle-Angle-Side) criterion, where two angles and a non-included side of one triangle are congruent to the corresponding parts of the other triangle.

Step3: Eliminate other options

SSS requires 3 congruent sides (no sides marked), SAS needs 2 sides and included angle (no sides marked), ASA needs 2 angles and included side (the congruent side here is not between the two same-marked angles). So only AAS applies.

Answer:

Yes by AAS