Introduction to Lines and Angles : āϏ⧰āϞ⧰⧇āĻ–āĻž āφ⧰⧁ āϕ⧋āĻŖā§° āĻĒā§°āĻŋāϚāϝāĻŧ


Point (āĻŦāĻŋāĻ¨ā§āĻĻ⧁)


A point determines a location. It has no size. āĻŦāĻŋāĻ¨ā§āĻĻā§ā§ąā§‡ āĻāϟāĻž āĻ…ā§ąāĻ¸ā§āĻĨāĻžāύ āύāĻŋā§°ā§āϧāĻžā§°āĻŖ āϕ⧰⧇āĨ¤ āχāϝāĻŧāĻžā§° āϕ⧋āύ⧋ āφāĻ•āĻžā§° āύāĻžāĻĨāĻžāϕ⧇āĨ¤


Example | āωāĻĻāĻžāĻšā§°āĻŖ: A dot (• P)


Line (āϏ⧰āϞ⧰⧇āĻ–āĻž)


A line extends infinitely in both directions. It has no endpoints.
āϏ⧰āϞ⧰⧇āĻ–āĻž āĻĻ⧁āϝāĻŧā§‹āĻĢāĻžāϞ⧇ āĻ…āϏ⧀āĻŽāϞ⧈ āĻŦāĻŋāĻ¸ā§āϤ⧃āϤ āĻšāϝāĻŧāĨ¤ āχāϝāĻŧāĻžā§° āϕ⧋āύ⧋ āĻļ⧇āώāĻŦāĻŋāĻ¨ā§āĻĻ⧁ āύāĻžāĻĨāĻžāϕ⧇āĨ¤


Example | āωāĻĻāĻžāĻšā§°āĻŖ: ↔ AB


Ray (ā§°āĻļā§āĻŽāĻŋ)


A ray has one endpoint and extends infinitely in one direction. ā§°āĻļā§āĻŽāĻŋā§° āĻāϟāĻž āĻļ⧇āώāĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨāĻžāϕ⧇ āφ⧰⧁ āχ āĻāϟāĻž āĻĻāĻŋāĻļāϤ āĻ…āϏ⧀āĻŽāϞ⧈ āĻŦāĻŋāĻ¸ā§āϤ⧃āϤ āĻšāϝāĻŧāĨ¤


Example | āωāĻĻāĻžāĻšā§°āĻŖ: → CD


Line Segment (⧰⧇āĻ–āĻžāĻ–āĻŖā§āĻĄ)


A line segment is a part of a line with two fixed endpoints. ⧰⧇āĻ–āĻžāĻ–āĻŖā§āĻĄ āĻšā§ˆāϛ⧇ āϏ⧰āϞ⧰⧇āĻ–āĻžā§° āĻāϟāĻž āĻ…āĻ‚āĻļ, āϝāĻžā§° āĻĻ⧁āϟāĻž āύāĻŋā§°ā§āĻĻāĻŋāĻˇā§āϟ āĻļ⧇āώāĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨāĻžāϕ⧇āĨ¤


Example | āωāĻĻāĻžāĻšā§°āĻŖ: E ───── F


Angle (āϕ⧋āĻŖ)


An angle is formed when two rays meet at a common point called the vertex. The rays are called the arms of the angle. āϝ⧇āϤāĻŋāϝāĻŧāĻž āĻĻ⧁āϟāĻž ā§°āĻļā§āĻŽāĻŋ āĻāϟāĻž āϏāĻžāϧāĻžā§°āĻŖ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϤ āĻŽāĻŋāϞāĻŋāϤ āĻšāϝāĻŧ, āϤ⧇āϤāĻŋāϝāĻŧāĻž āĻāϟāĻž āϕ⧋āĻŖ āϏ⧃āĻˇā§āϟāĻŋ āĻšāϝāĻŧāĨ¤ āϏ⧇āχ āϏāĻžāϧāĻžā§°āĻŖ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĻŸā§‹āĻ• āĻļā§€ā§°ā§āώāĻŦāĻŋāĻ¨ā§āĻĻ⧁ (Vertex) āφ⧰⧁ ā§°āĻļā§āĻŽāĻŋāĻĻ⧁āĻŸā§‹āĻ• āϕ⧋āĻŖā§° āĻŦāĻžāĻšā§ (Arms) āĻŦā§‹āϞāĻž āĻšāϝāĻŧāĨ¤


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  • Types of Angles : āϕ⧋āĻŖā§° āĻĒā§ā§°āĻ•āĻžā§° : Click Here

  • Complementary Angles (āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ) // Adjacent complementary angles. (āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖāĨ¤ : Click Here

  • Supplementary Angles (āϏāĻŽā§āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ) & Adjacent supplementary angles (āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āϏāĻŽā§āĻĒā§‚ā§°āĻ• āϕ⧋āĻŖ) : Click Here

  • Adjacent Angles & Linear Pair (āϏāĻ¨ā§āύāĻŋāĻšāĻŋāϤ āϕ⧋āĻŖ āφ⧰⧁ ⧰⧈āĻ–āĻŋāĻ• āϕ⧋āĻŖāϝ⧋⧰) : Click Here

  • Vertically Opposite Angles (āĻŦāĻŋāĻĒā§°ā§€āϤ āĻļā§€ā§°ā§āώ āϕ⧋āĻŖ) : Click Her

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

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

  • Transversal (āϛ⧇āĻĻāĻ• āϏ⧰āϞ⧰⧇āĻ–āĻž) : Click Here

  • Angles Made by a Transversal : āϛ⧇āĻĻāĻ• āϏ⧰āϞ⧰⧇āĻ–āĻžāχ āϏ⧃āĻˇā§āϟāĻŋ āϕ⧰āĻž āϕ⧋āĻŖāϏāĻŽā§‚āĻš : Click Here

  • Check the Parrallel Line (āϏāĻŽāĻžāĻ¨ā§āϤ⧰āĻžāϞ āϏ⧰āϞ⧰⧇āĻ–āĻž āĻĒā§°ā§€āĻ•ā§āώāĻž āϕ⧰āĻ•) : Solved Examples: : Click Here




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MCQs


1. A point has ______. / āĻāϟāĻž āĻŦāĻŋāĻ¨ā§āĻĻ⧁⧰ ______āĨ¤
(a) Length (b) Breadth (c) No size (d) Endpoints
Ans: (c) No size


2. A line extends infinitely in ______. / āϏ⧰āϞ⧰⧇āĻ–āĻž ______ āĻ…āϏ⧀āĻŽāϞ⧈ āĻŦāĻŋāĻ¸ā§āϤ⧃āϤ āĻšāϝāĻŧāĨ¤
(a) One direction (b) Both directions (c) Three directions (d) No direction
Ans: (b) Both directions


3. A ray has ______ endpoint(s). / āĻāϟāĻž ā§°āĻļā§āĻŽāĻŋā§° ______ āϟāĻž āĻļ⧇āώāĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨāĻžāϕ⧇āĨ¤
(a) No (b) One (c) Two (d) Three
Ans: (b) One


4. A line segment has ______ fixed endpoints. / āĻāϟāĻž āϰ⧇āĻ–āĻžāĻ–āĻŖā§āĻĄā§° ______ āϟāĻž āύāĻŋā§°ā§āĻĻāĻŋāĻˇā§āϟ āĻļ⧇āώāĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨāĻžāϕ⧇āĨ¤
(a) No (b) One (c) Two (d) Infinite
Ans: (c) Two


5. The common point where two rays meet is called the ______. / āĻĻ⧁āϟāĻž ā§°āĻļā§āĻŽāĻŋ āϝāĻŋ āϏāĻžāϧāĻžā§°āĻŖ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϤ āĻŽāĻŋāϞāĻŋāϤ āĻšāϝāĻŧ, āϤāĻžāĻ• ______ āĻŦā§‹āϞāĻž āĻšāϝāĻŧāĨ¤
(a) Arm (b) Vertex (c) Line (d) Segment
Ans: (b) Vertex