Question

Allison claims that the ABQ is similar to RPQ, given that AB and PR are parallel. Which of Allison's claims supporting her argument are correct? Select all that apply. 1 = 2 because they are vertically opposite angles. ABQ = QPR because they are corresponding angles. 1 = 2 because they are alternate interior angles. BAQ = QRP because they are alternate interior angles. ABQ and RPQ are not similar by AA similarity.

Answer 1

The two triangles are shown in the picture attached.

Let's see the important definitions you find in your options:
- alternate interior angles are found when two parallel lines are crossed by a transversal, and they are inside the two lines on opposite sides of the transversal;
- vertically opposite angles are found when two lines cross and they are the ones facing each other;
- corresponding angles are found when two parallel lines are crossed by a transversal, and they are on matching corners.

Looking at the picture we can say that:
a) 1 and 2 are vertically opposite angles;
b) ABQ and QPR are alternate interior angles;
c) BAQ and QRP are alternate interior angles.

Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles. 
BAQ = QRP because they are alternate interior angles. 

According to the AA similarity theorem, if two angles of a triangle are congruent to two angles of an other triangle, then the two triangles are similar. Therefore, Allison is right.