Question

which rule explains why these triangles are congruent?
image of two triangles with vertices y, x and w, v, intersecting at u, with marked congruent segments
options: sas, aas, asa, sss, these triangles cannot be proven congruent.

Explanation:

Step1: Identify Vertical Angles

Vertical angles at \( U \) are equal (\( \angle YUX \cong \angle WUV \)).

Step2: Identify Marked Sides

Two pairs of sides are marked equal: \( YU = VU \) and \( XU = WU \).

Step3: Apply SAS Criterion

We have two sides and the included angle equal (SAS: \( \text{Side-Angle-Side} \)). So by SAS, \( \triangle YUX \cong \triangle VUW \).

Answer:

These triangles can be proven congruent by the SAS rule. So the answer is the option labeled "SAS".