Difference between revisions of "Lines and Angles"

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=== Learning objectives ===
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[[Category:Mathematics]]
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''[https://karnatakaeducation.org.in/KOER/index.php/%E0%B2%B0%E0%B3%87%E0%B2%96%E0%B3%86%E0%B2%97%E0%B2%B3%E0%B3%81_%E0%B2%AE%E0%B2%A4%E0%B3%8D%E0%B2%A4%E0%B3%81_%E0%B2%95%E0%B3%8B%E0%B2%A8%E0%B2%97%E0%B2%B3%E0%B3%81 ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
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| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
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===Concept Map===
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[[File:Lines_and_Angles.mm|flash]]
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=== Additional Resources ===
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==== OER ====
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*Web resources:
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*Books and journals
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*Textbooks
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** NCERT Textbooks – [http://ncert.nic.in/textbook/textbook.htm?iemh1=7-15][http://ncert.nic.in/textbook/textbook.htm?iemh1=6-15 Class] 9
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*Syllabus documents
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==== Non-OER ====
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* Web resources:
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** [https://www.ck12.org/geometry/parallel-and-skew-lines/lesson/Parallel-and-Skew-Lines-BSC-GEOM/ CK12] - This website gives basic facts about parallel lines with examples and review questions.
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** [https://www.education.com/lesson-plan/angles-and-lines/ Education.com] - An exemplar for a lesson plan for lines and angles is on the web site.
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** [https://www.projectmaths.ie/documents/T&L/IntroductionToAngles.pdf Project Maths] - A detailed lesson plan for the topic is available in pdf format.
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** [https://teachers.net/lessons/posts/3404.html Teachers.net] - An exemplar for discussion based approach for to introduce lines and angles is shown.
 +
** [http://www.cpalms.org/Public/PreviewResourceLesson/Preview/73308 CLAMS] - This is an interactive lesson exploring Parallel and Perpendicular lines.
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** [https://www.ck12.org/geometry/parallel-and-skew-lines/lesson/Parallel-and-Skew-Lines-BSC-GEOM/ CK – 12] - Basic facts of parallel lines are discussed and introduced.
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** [http://jsuniltutorial.weebly.com/uploads/7/8/7/0/7870542/9th_geometry_mock_test_paper.pdf JsunilTutorial] - Worksheet for the chapter can be downloaded.
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*Books and journals
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*Textbooks
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**Karnataka Govt Text book – Class 8 : [http://ktbs.kar.nic.in/New/website%20textbooks/class8/8th-english-maths-1.pdf Part 1] , [http://ktbs.kar.nic.in/New/website%20textbooks/class8/8th-kannada-maths-2.pdf Part 2]
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*Syllabus documents
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*YouTube Videos
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Watch Video on Vertical Opposite angles  and Pair of Linear Equations
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{{#widget:YouTube|id=BRtNvXpZW6Y}}        {{#widget:YouTube|id=cUvL-tdRRDo}}
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Watch video on parallel lines and transversal
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{{#widget:YouTube|id=fo7EF2NNaak}}
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=== Learning Objectives ===
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* Introducing lines and line segments
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* Understanding formation of angles and their types
 +
* Differentiating parallel lines and skew lines
 +
* Recognizing angles pairs of angles formed in parallel lines
 +
 
 +
=== Teaching Outlines ===
 +
 
 +
==== Concept 1: Angles ====
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An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. angles can be classified according to the size of the angle.
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===== Activities =====
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[[Paper Folding Activity- Lines and Angles|Paper Folding Activity]]
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====== [[Introducing formation of angle]] ======
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The standard angle concept based on the relative inclination of two lines meeting at a point irrespective of length of arms is discussed in an exploratory method.
 +
 
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====== [[Types of angles]] ======
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We will learn the following types of angles: right angles, acute angles, obtuse angles, straight angles, reflex angles and complete angle.
 +
 
 +
==== Concept 2:  Pairs of angles ====
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In geometry, certain pairs of angles can have special relationships. Some examples are complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, corresponding angles and adjacent angles.
 +
 
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===== Activities =====
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====== [[Intersection of two lines]] ======
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====== [[Adjacent angles]] ======
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Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle.
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====== [[Complementary angles]] ======
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Complementary angles are two angles with a sum of 90°. A common case is when they form a right angle.
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====== [[Supplementary angles]] ======
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Supplementary angles are two angles with a sum of 180°. A common case is when they lie on the same side of a straight line.
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====== [[Vertically opposite angles]] ======
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When two straight lines intersect each other four angles are formed.The pair of angles which lie on the opposite sides of the point of intersection are  vertically opposite angles.
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====== [[Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180 degrees|Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180<sup>o</sup>]] ======
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Two adjacent angles are said to be form a linear pair of angles, if their non-common arms are two opposite rays. Linear pair axiom of theorems are if a ray stands on a line , then the sum of two adjacent angles so formed is 180 degree
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====== [[Linear pair axiom : If the sum of two adjacent angles is 180 degrees, then the non-common arms of the angles form a line|Linear pair axiom : If the sum of two adjacent angles is 180<sup>o</sup>, then the non-common arms of the angles form a line]] ======
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 +
==== Concept 3: Parallel lines ====
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Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel.
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===== Activities =====
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====== [[Introducing parallel lines|Introducing parallel lines]] ======
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Parallel lines are lines that are always the same distance apart. Because they are always the same distance from one another, parallel lines will never intersect.
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====== [[Parallel lines 1|Parallel lines activity1]] ======
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====== [[Angles associated with parallel lines]] ======
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Two parallel lines are cut by a transversal  the angles formed are alternate angles, corresponding angles co-interior angles and vertically opposite angles.
 +
 
 +
====== [[Parallel lines|Parallel lines and measures of angles formed]] ======
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The relation between angles that are formed in multiple parallel lines is investigated with geogebra sketch.
 +
 
 
[[Category:Class 9]]
 
[[Category:Class 9]]
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[[Category:Lines and Angles]]
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=== Activity No # 1 ===
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[[Category:Class 8]]
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* Estimated Time - 40 minutes
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[[Category:Class 10]]
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* Materials/ Resources needed; Paper, pencil, and scale.
 
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* Prerequisites/Instructions, if any:
 
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# The students should know points and line segments.
 
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* Multimedia resources
 
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* Website interactives/ links/ Geogebra Applets
 
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* Process (How to do the activity):
 
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# Mark three non-collinear point P, Q and R on a paper.
 
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# Join these points in all possible ways. The segments are PQ, QR and RP.
 
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# A simple close curve formed by these three segments is called a triangle. It is named in one of the following ways.
 
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# Triangle PQR or Triangle PRQ or Triangle QRP or Triangle RPQ or Triangle RQP .
 
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* Developmental Questions (What discussion questions):
 
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# What are plane figures ?
 
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# What is a polygon ?
 
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# How many points are needed to make a traingle ?
 
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* Evaluation (Questions for assessment of the child):
 

Latest revision as of 14:36, 10 August 2023

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

[maximize]

Additional Resources

OER

  • Web resources:
  • Books and journals
  • Textbooks
  • Syllabus documents

Non-OER

  • Web resources:
    • CK12 - This website gives basic facts about parallel lines with examples and review questions.
    • Education.com - An exemplar for a lesson plan for lines and angles is on the web site.
    • Project Maths - A detailed lesson plan for the topic is available in pdf format.
    • Teachers.net - An exemplar for discussion based approach for to introduce lines and angles is shown.
    • CLAMS - This is an interactive lesson exploring Parallel and Perpendicular lines.
    • CK – 12 - Basic facts of parallel lines are discussed and introduced.
    • JsunilTutorial - Worksheet for the chapter can be downloaded.
  • Books and journals
  • Textbooks
  • Syllabus documents
  • YouTube Videos

Watch Video on Vertical Opposite angles and Pair of Linear Equations

Watch video on parallel lines and transversal

Learning Objectives

  • Introducing lines and line segments
  • Understanding formation of angles and their types
  • Differentiating parallel lines and skew lines
  • Recognizing angles pairs of angles formed in parallel lines

Teaching Outlines

Concept 1: Angles

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. angles can be classified according to the size of the angle.

Activities

Paper Folding Activity

Introducing formation of angle

The standard angle concept based on the relative inclination of two lines meeting at a point irrespective of length of arms is discussed in an exploratory method.

Types of angles

We will learn the following types of angles: right angles, acute angles, obtuse angles, straight angles, reflex angles and complete angle.

Concept 2: Pairs of angles

In geometry, certain pairs of angles can have special relationships. Some examples are complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles, corresponding angles and adjacent angles.

Activities
Intersection of two lines
Adjacent angles

Adjacent angles are two angles that have a common vertex and a common side. The vertex of an angle is the endpoint of the rays that form the sides of the angle.

Complementary angles

Complementary angles are two angles with a sum of 90°. A common case is when they form a right angle.

Supplementary angles

Supplementary angles are two angles with a sum of 180°. A common case is when they lie on the same side of a straight line.

Vertically opposite angles

When two straight lines intersect each other four angles are formed.The pair of angles which lie on the opposite sides of the point of intersection are vertically opposite angles.

Linear pair axiom : If a ray stands on a line, then the sum of two adjacent angles so formed is 180o

Two adjacent angles are said to be form a linear pair of angles, if their non-common arms are two opposite rays. Linear pair axiom of theorems are if a ray stands on a line , then the sum of two adjacent angles so formed is 180 degree

Linear pair axiom : If the sum of two adjacent angles is 180o, then the non-common arms of the angles form a line

Concept 3: Parallel lines

Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel.

Activities
Introducing parallel lines

Parallel lines are lines that are always the same distance apart. Because they are always the same distance from one another, parallel lines will never intersect.

Parallel lines activity1
Angles associated with parallel lines

Two parallel lines are cut by a transversal  the angles formed are alternate angles, corresponding angles co-interior angles and vertically opposite angles.

Parallel lines and measures of angles formed

The relation between angles that are formed in multiple parallel lines is investigated with geogebra sketch.

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