Pairs of Lines (āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āϝ⧋⧰)


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 || q) (read as: line p is parallel to line q).
āχāϝāĻŧāĻžāĻ• (p || 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


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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) Perpendicular bisector
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) Vertex (c) Point of intersection (d) Endpoint


 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) Increasing (b) Decreasing (c) Constant (d) Zero
Ans: (c) Constant


5. Which symbol represents parallel lines ? / āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻžāĻ• āϕ⧋āύāĻŸā§‹ āϚāĻŋāĻšā§āύ⧇⧰⧇ āĻĒā§ā§°āĻ•āĻžāĻļ āϕ⧰āĻž āĻšāϝāĻŧ ?
(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) Hands of a clock (b) Railway tracks (c) Letter X (d) Scissors
Ans: (b) Railway tracks


7. Which of the following is an example of intersecting lines ? / āϤāϞ⧰ āϕ⧋āύāĻŸā§‹ āϛ⧇āĻĻāύāĻ•āĻžā§°ā§€ āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āωāĻĻāĻžāĻšā§°āĻŖ ?
(a) Railway tracks (b) Opposite edges of a ruler (c) Scissors (d) Book edges
Ans: (c) Scissors


8. If two lines intersect, they have ______ point(s) in common. / āϝāĻĻāĻŋ āĻĻ⧁āϟāĻž āϏ⧰āϞ⧰⧇āĻ–āĻžāχ āĻĒā§°āĻ¸ā§āĻĒā§°āĻ• āϛ⧇āĻĻ āϕ⧰⧇, āϤ⧇āĻ¨ā§āϤ⧇ āϏāĻŋāĻšāρāϤ⧰ āĻ•āĻŋāĻŽāĻžāύāϟāĻž āϏāĻžāϧāĻžā§°āĻŖ āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨāĻžāϕ⧇ ?
(a) No (b) One (c) Two (d) Infinite
Ans: (b) One