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 _____?
Check your 7-25-11,9:25am post.
To prove that angles ABC and RPQ are congruent, we can use the fact that triangle ABC is congruent to triangle RPQ. Since corresponding parts of congruent triangles are congruent, we know that corresponding angles are congruent as well.
To fill in the blanks in the proof:
Angle ABC is congruent to RPQ by the Corresponding Angles Postulate.
Angles ABC and RPQ are congruent by the Corresponding Angles Postulate and the fact that triangle ABC is congruent to triangle RPQ.