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.
1 answer:
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.
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.
You might be interested in
<h2>Hello!</h2>
The answer is: There is a total of 5.797 gallons pumped during the given period.
<h2>Why?</h2>To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)
The given function is:
So, the integral will be:
So, integrating we have:
Performing a change of variable, we have:
Then, substituting, we have:
Reverting the change of variable, we have:
Then, evaluating we have:
So, there is a total of 5.797 gallons pumped during the given period.
Have a nice day!