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

Question

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 (?).

Answer 1

((AB)^2 = (5-3)^2 + (2-(-1))^2 = 13,
AB = sqrt(13).

AB = RP = sqrt(13).

BC = PQ = sqrt(53).

CA = QR = sqrt(26).

AB Congruent to RP.

Triangle ABC is Congruent to Triangle
RPQ by S.S.S.

Angle ABC is Congruent to angle RPQ by Correspondant angles of Congruent
triangles.