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Lines and Angles (view source)

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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.
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** [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
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* Differentiating parallel lines and skew lines
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* Recognizing angles pairs of angles formed in parallel lines
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=== Teaching Outlines ===
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==== 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.
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==== 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.
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====== [[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.
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[[Category:Class 9]]
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[[Category:Lines and Angles]]
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[[Category:Class 8]]
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[[Category:Class 10]]
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