Question

Allison claims that the (triangle)ABQ is similar to (triangle)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. (triangle)ABQ  and (triangle) RPQ  are not similar by  AA  similarity.

Answer 1

I draw the two triangles, see the picture attached.

As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.

Angles ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.

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

Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.