Parallel Lines Geometry
Posted by
Ravi Kumar at Sunday, March 28, 2010
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When a straight line XY cuts two parallel line PQ and RS [as shown in figure], the following are the relationships between various angles that are formed. [M and N are the points of intersection of XY with PQ and RS respectively].
a) alternate angles are equal
i.e, angle PMN = angle MNS
angle QMN = angle MNR
b) corresponding angles are equal
i.e, angle XMQ = angle MNS
angle QMN = angle SNY
angle XMP = angle MNR
angle PMN = angle RNY
c) Sum of interior angles on the same side of cutting line is equal to 180⁰
i.e, angle QMN + angle MNS = 180⁰
angle PMN + angle MNR = 180⁰
d) Sum of exterior angles on the same side of transversal line is equal to 180⁰
i.e, angle XMQ + angle SNY = 180⁰
angle XMP + angle RNY = 180⁰
If three or more parallel lines make equal intercepts on one transversal, they make equal intercepts on any other transversal as well.