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Svetach [21]
3 years ago
5

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.

Mathematics
1 answer:
S_A_V [24]3 years ago
3 0
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 <span>ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by </span><span>two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.</span>

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. 

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