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