Question 822137: I have a 2 column proof for my geometry homework, I had another but already figured it out, but this one is still giving me trouble, even after reading over the lesson
Here's the shape http://i.imgur.com/S6tJc3P.png
Given: Segment AB || Segment PQ
Segment AB is congruent to Segment PQ
Prove: Segment BZ is congruent to Segment ZQ
Can you help me walk through it? thanks!
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website! Extend the segments so that there are multiple angles at A , B and C .
Assign numbers to angles, beginning with angle ABZ. Call
angle ABZ, angle 1. Around B, label the angles clockwise as angles
2, 3 and 4.
Around A, begin with angle ZAB, label it as 5. Label clockwise 6 , 7 and 8.
Around P, begin with angle ZPQ, label it as 9. Label clockwise 10, 11 and 12.
Around Q, begin with angle ZQP, label it as 13. Label clockwise 14, 15 and 16.
Angle 4 = angle 14, corresponding angles of diagonal intersecting || lines.
Angle 1 = angle 13, supplementary angles.
Angle 8 = angle 10, corresponding angles of diagonal intersecting || lines.
Angle 9 = angle 5, supplementary angles.
So ABZ is congruent with QPZ , by angle/side/angle.
BZ congruent with ZQ since these sides are opposite angels 5 and 9 of congruent
triangles.
I hope this helps.
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