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.
