Posted by **Wendell** on Tuesday, July 26, 2011 at 8:59pm.

Given: A(3,-1), B(5,2), C(-2,0), P(-3,4), Q(-5,-3), R(-6,2).

Prove: angles ABC and RPQ are congruent by completing the paragraph proof.

AB=RP=13, BC=(?)=53, and CA=QR=26. So segment AB is congruent to (?), segments BC and PQ are congruent and segment CA is congruent to segment QR. Therefore triangle ABC is congruent to (?) by (?), and angles ABC and RPQ are congruent by (?).

AB = ã[(5-3)^2 + (2+1)^2] = ã(4+9) = ã13

RP = ã([-3+6)^2 +(4-2)^2] = ã(9+4) = ã13

BC = ã[(5+2)^2 + (2-0)^2] = ã(49+4) = ã53

PQ = ã[-3+5)^2 + (4+3)^2] = ã(4+49) = ã53

AC = ã[3+2)^2 + (-1-0)^2] = ã(25+1) = ã26

RQ = ã[(-6+5)^2 + (2+3)^2] = ã(1+25) = ã26

clearly we have corresponding pairs of sides equal, so by SSS, ∆ABC≅∆RPQ

I guess I don't understand how to write the answer.

Angle ABC is congruent to RPQ by____? and angles ABC and RPQ are congruent by _____?

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