Question

which rule explains why these triangles are similar? sss sas aa none of the above; the triangles cannot be proven similar

Explanation:

Step1: Recall triangle similarity rules

SSS (Side - Side - Side) similarity requires the ratios of all three pairs of corresponding sides to be equal. SAS (Side - Angle - Side) similarity requires the ratio of two pairs of corresponding sides to be equal and the included angles to be congruent. AA (Angle - Angle) similarity requires two pairs of corresponding angles to be congruent.

Step2: Analyze the given triangles

In triangle \(HIG\), two angles (\(\angle I\) and \(\angle G\)) are marked. In triangle \(TUV\), two angles (\(\angle U\) and \(\angle T\)) are marked. If two angles of one triangle are congruent to two angles of another triangle, then the third angles must also be congruent (since the sum of angles in a triangle is \(180^{\circ}\)).

Answer:

AA