Pairs of Lines (āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āϝ⧋⧰) // Parallel Lines (āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻž)


1. Intersecting Lines (āϛ⧇āĻĻāύāĻ•āĻžā§°ā§€ āϏ⧰āϞ⧰⧇āĻ–āĻž)


Two lines that meet at a common point are called intersecting lines.
āĻāϕ⧇ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϤ āĻŽāĻŋāϞāĻŋāϤ āĻšā§‹ā§ąāĻž āĻĻ⧁āϟāĻž āϏ⧰āϞ⧰⧇āĻ–āĻžāĻ• āϛ⧇āĻĻāύāĻ•āĻžā§°ā§€ āϏ⧰āϞ⧰⧇āĻ–āĻž (Intersecting Lines) āĻŦā§‹āϞāĻž āĻšāϝāĻŧāĨ¤


The point P is called the point of intersection.
P āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĻŸā§‹āĻ• āϛ⧇āĻĻāύāĻŦāĻŋāĻ¨ā§āĻĻ⧁ (Point of Intersection) āĻŦā§‹āϞāĻž āĻšāϝāĻŧāĨ¤


2. Parallel Lines (āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻž)


Two lines that never meet, even when extended indefinitely, are called parallel lines. The distance between them is always constant.
āϝāĻŋ āĻĻ⧁āϟāĻž āϏ⧰āϞ⧰⧇āĻ–āĻžāχ āĻ…āϏ⧀āĻŽāϞ⧈ āĻŦ⧃āĻĻā§āϧāĻŋ āϕ⧰āĻŋāϞ⧇āĻ“ āϕ⧇āϤāĻŋāϝāĻŧāĻžāĻ“ āĻŽāĻŋāϞāĻŋāϤ āύāĻšāϝāĻŧ, āϏ⧇āχāĻŦā§‹ā§°āĻ• āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻž (Parallel Lines) āĻŦā§‹āϞāĻž āĻšāϝāĻŧāĨ¤ āϏāĻŋāĻšāρāϤ⧰ āĻŽāĻžāϜ⧰ āĻĻā§‚ā§°āĻ¤ā§āĻŦ āϏāĻĻāĻžāϝāĻŧ āϏāĻŽāĻžāύ āĻĨāĻžāϕ⧇āĨ¤


We write (p âˆĨ q) (read as: line p is parallel to line q).
āχāϝāĻŧāĻžāĻ• (p âˆĨ q) āϞāĻŋāĻ–āĻž āĻšāϝāĻŧ (āĻĒāĻĸāĻŧāĻž āĻšāϝāĻŧ: p āϏ⧰āϞ⧰⧇āĻ–āĻž q āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ)āĨ¤


Examples | āωāĻĻāĻžāĻšā§°āĻŖ: Railway tracks (⧰⧇āϞāĻĒāĻĨā§° ⧰⧇āϞāϞāĻžāχāύ), Opposite edges of a ruler (āĻ¸ā§āϕ⧇āϞ⧰ āĻŦāĻŋāĻĒā§°ā§€āϤ āĻ•āĻžāώ)āĨ¤


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MCQs: Pairs of Lines


1. Two lines that meet at a common point are called ______. / āĻāϕ⧇ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϤ āĻŽāĻŋāϞāĻŋāϤ āĻšā§‹ā§ąāĻž āĻĻ⧁āϟāĻž āϏ⧰āϞ⧰⧇āĻ–āĻžāĻ• āĻ•āĻŋ āĻŦā§‹āϞāĻž āĻšāϝāĻŧ ?
(a) Parallel lines (b) Intersecting lines (c) Transversal (d) Rays
Ans: (b) Intersecting lines


2. The common point where two lines meet is called the ______. / āĻĻ⧁āϟāĻž āϏ⧰āϞ⧰⧇āĻ–āĻž āϝāĻŋ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϤ āĻŽāĻŋāϞāĻŋāϤ āĻšāϝāĻŧ, āϏ⧇āχ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĻ• āĻ•āĻŋ āĻŦā§‹āϞāĻž āĻšāϝāĻŧ ?
(a) Midpoint (b) Endpoint (c) Point of intersection (d) Vertex
Ans: (c) Point of intersection


3. Two lines that never meet, even when extended indefinitely, are called ______. / āĻ…āϏ⧀āĻŽāϞ⧈ āĻŦ⧃āĻĻā§āϧāĻŋ āϕ⧰āĻŋāϞ⧇āĻ“ āϕ⧇āϤāĻŋāϝāĻŧāĻžāĻ“ āĻŽāĻŋāϞāĻŋāϤ āύ⧋āĻšā§‹ā§ąāĻž āĻĻ⧁āϟāĻž āϏ⧰āϞ⧰⧇āĻ–āĻžāĻ• āĻ•āĻŋ āĻŦā§‹āϞāĻž āĻšāϝāĻŧ ?
(a) Intersecting lines (b) Parallel lines (c) Transversal (d) Perpendicular lines
Ans: (b) Parallel lines


4. The distance between two parallel lines is always ______. / āĻĻ⧁āϟāĻž āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āĻŽāĻžāϜ⧰ āĻĻā§‚ā§°āĻ¤ā§āĻŦ āϏāĻĻāĻžāϝāĻŧ ______āĨ¤
(a) Zero (b) Variable (c) Constant (d) Increasing
Ans: (c) Constant


5. Which symbol represents parallel lines ? / āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āϚāĻŋāĻšā§āύ āϕ⧋āύāĻŸā§‹ ?
(a) ⊥ (b) = (c) âˆĨ (d) ×
Ans: (c) âˆĨ


6. Which of the following is an example of parallel lines ? / āϤāϞ⧰ āϕ⧋āύāĻŸā§‹ āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āωāĻĻāĻžāĻšā§°āĻŖ ?
(a) Scissors (b) Railway tracks (c) Clock hands (d) Letter X
Ans: (b) Railway tracks


7. Opposite edges of a ruler are an example of ______. / āĻ¸ā§āϕ⧇āϞ⧰ āĻŦāĻŋāĻĒā§°ā§€āϤ āĻ•āĻžāώāϏāĻŽā§‚āĻš ______-ā§° āωāĻĻāĻžāĻšā§°āĻŖāĨ¤
(a) Intersecting lines (b) Parallel lines (c) Rays (d) Line segments
Ans: (b) Parallel lines


8. Intersecting lines have ______ common point(s). / āϛ⧇āĻĻāύāĻ•āĻžā§°ā§€ āϏ⧰āϞ⧰⧇āĻ–āĻžā§° ______ āϟāĻž āϏāĻžāϧāĻžā§°āĻŖ āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨāĻžāϕ⧇āĨ¤
(a) No (b) One (c) Two (d) Infinite
Ans: (b) One