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From Karnataka Open Educational Resources
→Solved problems/ key questions (earlier was hints for problems).
=== Concept Map ===
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story 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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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
===Concept Map===
[[File:Lines_and_Angles.mm|flash]]
=== Additional Resources ===
=== Additional Resources ===
==== OER ====
==== OER ====
*Web resources:
*Books and journals
*Textbooks
** NCERT Textbooks – [http://ncert.nic.in/textbook/textbook.htm?iemh1=7-15][http://ncert.nic.in/textbook/textbook.htm?iemh1=6-15 Class] 9
*Syllabus documents
==== Non-OER ====
==== Non-OER ====
* Web resources:
** [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.
** [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.
** [https://www.projectmaths.ie/documents/T&L/IntroductionToAngles.pdf Project Maths] - A detailed lesson plan for the topic is available in pdf format.
** [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.
** [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.
** [http://jsuniltutorial.weebly.com/uploads/7/8/7/0/7870542/9th_geometry_mock_test_paper.pdf JsunilTutorial] - Worksheet for the chapter can be downloaded.
*Books and journals
*Textbooks
**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]
*Syllabus documents
*YouTube Videos
Watch Video on Vertical Opposite angles and Pair of Linear Equations
{{#widget:YouTube|id=BRtNvXpZW6Y}} {{#widget:YouTube|id=cUvL-tdRRDo}}
Watch video on parallel lines and transversal
{{#widget:YouTube|id=fo7EF2NNaak}}
=== Learning Objectives ===
=== 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 ===
=== Teaching Outlines ===
==== Concept 1: Angles ====
==== 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 =====
===== Activities =====
[[Paper Folding Activity- Lines and Angles|Paper Folding Activity]]
====== '''[[Introducing formation of angle]]''' ======
====== [[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]]''' ======
====== [[Types of angles]] ======
We will learn the following types of angles: right angles, acute angles, obtuse angles, straight angles, reflex angles and complete angle.
====== Pairs of angles ======
==== 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.
====== '''[[Adjacent angles]]''' ======
===== Activities =====
====== '''[[Complementary angles]]''' ======
====== [[Intersection of two lines]] ======
====== '''[[Supplementary angles]]''' ======
====== [[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.
====== '''[[Vertically opposite angles]]''' ======
====== [[Complementary angles]] ======
Complementary angles are two angles with a sum of 90°. A common case is when they form a right angle.
====== '''[[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>]]''' ======
====== [[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.
====== '''[[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]]''' ======
====== [[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.
==== Concept 2: '''Parallel lines''' ====
====== [[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>]] ======
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
====== [[Introducing parallel lines]] ======
====== [[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]] ======
====== '''[[Angles associated with parallel lines]]''' ======
==== 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 =====
====== '''[[Parallel lines|Parallel lines and measures of angles formed]]''' ======
====== [[Introducing parallel lines|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 1|Parallel lines activity1]] ======
===== Solved problems/ key questions (earlier was hints for problems). =====
====== [[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.
=== Projects (can include math lab/ science lab/ language lab) ===
====== [[Parallel lines|Parallel lines and measures of angles formed]] ======
The relation between angles that are formed in multiple parallel lines is investigated with geogebra sketch.
[[Category:Class 9]]
[[Category:Lines and Angles]]
[[Category:Class 8]]
[[Category:Class 10]]
