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## Theorems

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**Parallel**Line Theorems**Parallel Line Theorems**Two parallel lines on their own are not vary interesting to us in terms of geometry. But if straight line (called a transversal) intersects two parallel lines, then the angles created are very interesting to us…..**These lines are parallel because they will never cross….**The dashed line is called a transversal, because it crosses both lines**As soon as the transversal is drawn, a collection of angles**are created. These angles are equal because of OAT. Copy these to your sheet. x y x y x x y y In this diagram, there is a collection of patterns that can be generated.**y**y “Z” pattern (alternate angles: AA)**x**x “Z” pattern**y**x x y “F” pattern (corresponding angles: CA)**x**y x y “F” pattern**y**x X + Y = 180O x y “C” pattern (supplementary angles: SA) ( also called interior angles )**Find X,Y and Z**Statement Reason 70O Z Z = 70O OAT Y = 180O – 70O SA = 110O Y X X = 110O OAT