So we really translated more than just line m. (image on the top left)Īnother student suggested translating line m using vector BE. That didn’t get us very far in showing that the corresponding angles are congruent. Then we created a parallel to lines m and n through X.
One student suggested constructing the midpoint, X, of segment BE. Can we use rigid motions to show that the corresponding angles are congruent? Then once we’ve allowed those, it’s not too bad to prove that alternate interior angles are congruent when parallel lines are cut by a transversal.īut we wonder whether we have to let corresponding angles in as a postulate. It makes sense to students that the corresponding angles are congruent.
SUPPLEMENTARY ANGLE PROOFS SOFTWARE
We use dynamic geometry software to explore Parallel Lines and Transversals:Īnd then traditionally, we have allowed corresponding angles congruent when parallel lines are cut by a transversal as the postulate in our deductive system. If a straight line crossing two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if extended indefinitely, meet on that side on which are the angles less than the two right angles. We make sense of Euclid’s 5 th Postulate (wording below from Cut the Knot): My students come to high school geometry having experience with angle measure relationships when parallel lines are cut by a transversal.
Theorems include: vertical angles are congruent when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Īfter proving that vertical angles are congruent, we turned our attention towards angles formed by parallel lines cut by a transversal.
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