Question

for questions 10 - 13, determine (if possible)
10.
a. aa~
b. sss~
c. sas~
d. not similar

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. In the given figure, the two triangles have a pair of vertical angles which are congruent.

Step2: Use AA similarity criterion

The AA (Angle - Angle) similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Here, we have one pair of vertical angles (equal) and we can assume the other pair of angles (due to the parallel - like arrow markings which imply some angle relationships, but even without side lengths, the presence of one pair of equal angles (vertical angles) and if we consider the non - vertical angles, since the lines are drawn in a way that suggests another pair of equal angles (by the nature of the figure's construction, if we assume the lines are parallel - like, alternate interior angles could be equal, but even without that, for the AA criterion, we just need two pairs of equal angles. Since vertical angles are one pair and if we consider the other two angles (the non - vertical ones in each triangle), they can be considered as another pair (by the AA similarity concept where if two angles are equal, the third is also equal as the sum of angles in a triangle is \(180^{\circ}\)).

Answer:

A. AA~