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Properties of parallel lines Meaning of Parallel lines: These are lines in one plane which do not meet and they have the property that they are everywhere the same distance apart. N Y B x A y X In the figure above, AX and BY are parallel lines. The line NBA cutting the parallel lines at A and B is called a transversal. Angles NBY, BAX are called corresponding angles. The angles x and y are called alternate angles. - corresponding angles are equal. - Alternate angles are equal. Interior angles The figure below shows a pair of shaded angles on the same side of a transversal and lying between the parallel lines. This is a pair of interior angles. These interior angles are supplementary angles. Example 1. Find angles s and t in the diagram.
t s 75 0 Solution s and 75 0 are vertically opposite angles so s = 75 0 . t and 75 0 are corresponding angles so t = 75 0 . Exercise Find the angles marked a and b in the diagram. a 140 0 b 1. In the figure below if a = 27 0 , and b= 56 0 , calculate angle BCX, XCD and BCY. B A a X D b C Y E 2. In the diagram, if AB is parallel to DC and AD is parallel to BC, and b = 61 0 . Calculate a, c and d. 3. In the figure BCD is a straight line. a = 50 0 and b = 35 0 . Calculate angles XCD, ACX and ACB.
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