Question

which rule explains why these triangles are congruent?

two triangles, xyz and vwu, with markings: xy and vu have one red tick, angles at y and v have two red arcs, angles at x and u have one red arc

options:
sas
aas
asa
sss
these triangles cannot be proven congruent.

Explanation:

To determine the congruence rule, we analyze the markings:

• In triangle \( XYZ \) and \( VWU \), we have a pair of equal angles (the single - arc angles), a pair of equal sides (the marked sides), and another pair of equal angles (the double - arc angles).
• The ASA (Angle - Side - Angle) congruence rule states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent. Here, the side is between the two angles, so the ASA rule applies.

Answer:

ASA