If two lines and a transversal form a pair of equal alternate-interior angles, then the lines are parallel.
So, given that AB and CD are line segments crossed by a transversal at P and Q and that angles APQ = PQD
Thursday, November 6, 2008
Homework due 11/7/08
By completing the proof below you will be proving the following theorem:
So, given that AB and CD are line segments crossed by a transversal at P and Q and that angles APQ = PQD, prove that AB is parallel to CD.
So, given that AB and CD are line segments crossed by a transversal at P and Q and that angles APQ = PQD
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4 comments:
Hint: You will need an auxiliary line and the notion of congruence of triangles. Also, do not make the mistake of assuming that AB and CD are of the same length.
Also, when considering the auxiliary line, consider the theorem we proved at the beginning of last class.
Michael originally did it and helped me do it by counterprooving that the two angles formed by line ab and cd and the line intersecting both of them got the triangle to have 180 degrees in two angles. we did this by prooving that the supplements of both given angles are the same and the given angle plus the supplement (both are inside the triangle) equal 180 degrees
Great work Michael and Jack. You have proof that makes a very good case for Euclid's parallel postulate.
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