Posted by Wendell on .
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 (?).

Geometry 
Reiny,
AB = √[(53)^2 + (2+1)^2] = √(4+9) = √13
RP = √([3+6)^2 +(42)^2] = √(9+4) = √13
BC = √[(5+2)^2 + (20)^2] = √(49+4) = √53
PQ = √[3+5)^2 + (4+3)^2] = √(4+49) = √53
AC = √[3+2)^2 + (10)^2] = √(25+1) = √26
RQ = √[(6+5)^2 + (2+3)^2] = √(1+25) = √26
clearly we have corresponding pairs of sides equal, so
by SSS, ∆ABC≅∆RPQ
(Your length of 13, 53, and 26 should have been √13, √53, and √26) 
Geometry 
Wendell,
I guess I don't understand how to write the answer.

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