MyMaths MyLife

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.

Important Facts:

Direct Proportion: Two Quantities are said to be directly
proportional, if on the increase (or decrease) of the one, the
other increases(or decreases) to the same extent.

Ex:(i) Cost is directly proportional to the number of articles.
(More articles, More cost).

(ii) Work done is directly proportional to the number of men
working on it. (More men, more work).

Indirect Proportion: Two Quantities are said to be
indirectly proportional,if on the increase of the one , the other
decreases to the same extent and vice-versa.

Ex:(i) The time taken by a car covering a certain distance is
inversely proportional to the speed of the car.(More speed,
less is the time taken to cover the distance).

(ii) Time taken to finish a work is inversely proportional to
the number of persons working at it.
(More persons, less is the time taken to finish a job).

Note: In solving Questions by chain rule, we compare every
item with the term to be found out.