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Line 1: − + − <!-- BANNER ACROSS TOP OF PAGE -->+ − {| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;" − |- − | 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:_History The Story of Mathematics] − | 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] − | style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " | − − | 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/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus] − | 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:_Topics Topics in School Mathematics] − | 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/Text_Books#Mathematics_-_Textbooks Textbooks] − | 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/Maths:_Question_Papers Question Bank] − |} − While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist''']. − + − [[File:Triangles.mm]]+ − − ===Additional Resources=== − ====OER==== − * Web resources: − ** [https://en.wikipedia.org/wiki/Triangle Wikipedia, the free encyclopedia] : The website gives a comprehensive information on triangles from basics to in depth understanding of the topic. − ** [https://jsuniltutorial.weebly.com/ix-triangles.html cbsemathstudy.blogspot.com] : The website contains worksheets that can be downloaded. Worksheets for other chapters can also be searched for which are listed based on class. − − * Books and journals − * Textbooks − ** NCERT Textbooks – [http://ncert.nic.in/textbook/textbook.htm?iemh1=7-15 Class 9] − − * Syllabus documents − − ====Non-OER==== − * Web resources: − ** [https://www.brighthubeducation.com/middle-school-math-lessons/39674-triangle-properties-and-angles/ Bright hub education] : The website describes a lesson plan for introducing triangles and lists classroom problems at the end of the lesson that can be solved for better understanding. − ** [http://www.cpalms.org/Public/PreviewResourceLesson/Preview/40261 CPALMS] : The website contains lesson plan, activities and worksheets associated with triangles. − ** [https://www.urbanpro.com/cbse-class-9-maths-construction UrbanPro] : This website gives downloadable worksheets with problems on triangle construction. − ** [https://schools.aglasem.com/59755 AglaSem Schools] : This website lists important questions for math constructions. − ** [http://www.nios.ac.in/media/documents/SecMathcour/Eng/Chapter-12.pdf National Institute of Open Schooling]: This website has good reference notes on concurrency of lines in a triangle for both students and teachers. − ** [http://www.mathopenref.com/ Math Open Reference] : This website gives activities that can be tried and manipulated online for topics on geometry. − − * 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 (CBSE, ICSE, IGCSE etc) Line 70:
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<!-- This portal was created using subst:box portal skeleton -->
<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;">
''[https://karnatakaeducation.org.in/KOER/index.php/%e0%b2%a4%e0%b3%8d%e0%b2%b0%e0%b2%bf%e0%b2%ad%e0%b3%81%e0%b2%9c%e0%b2%97%e0%b2%b3%e0%b3%81 ಕನ್ನಡ]''</div>
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
===Concept Map ===
===Concept Map===
{{#drawio:mmTriangles|interactive}}
===Learning Objectives===
===Learning Objectives===
Interior angles are angles that are formed with in the closed figure by the adjacent sides. An exterior angle is an angle formed by a side and the extension of an adjacent side. Exterior angles form linear pairs with the interior angles.
Interior angles are angles that are formed with in the closed figure by the adjacent sides. An exterior angle is an angle formed by a side and the extension of an adjacent side. Exterior angles form linear pairs with the interior angles.
[[Category:Triangles]]
[[Category:Triangles]]
[[Category:Class 8]]
[[Category:Class 10]]
==== Concept #: Types of triangles based on sides and angles ====
==== Concept #: Types of triangles based on sides and angles ====
Variations in elements that make a triangle results in distinct triangles. Recognizing these variations helps in interpreting changes that are possible with in a triangle.
Variations in elements that make a triangle results in distinct triangles. Recognizing these variations helps in interpreting changes that are possible with in a triangle.
'''Video resource:''' Explanation of Types of Triangles by NCERT
{{Youtube|SXYZd536Vao
}}
===== Activities # =====
===== Activities # =====
====== [[Angle sum property]] ======
====== [[Angle sum property]] ======
Interior angles of a triangle are in relation and also determine the type of angles that can forms a triangle. This also helps in determining an unknown angle measurement.
Interior angles of a triangle are in relation and also determine the type of angles that can forms a triangle. This also helps in determining an unknown angle measurement.
'''Video resource:''' Classroom activity for angle sum property of Triangle by NCERT
{{Youtube|BRDAXvQlzt0
}}
====== [[Angle sum property of a Triangle]] ======
====== [[Relation between interior and exterior angles in triangle|Exterior angle theorem]] ======
====== [[Relation between interior and exterior angles in triangle|Exterior angle theorem]] ======
Interior angle and the corresponding angle form a linear pair. This exterior angle in relation to the remote interior angles and their dependencies are deducted with the theorem.
Interior angle and the corresponding angle form a linear pair. This exterior angle in relation to the remote interior angles and their dependencies are deducted with the theorem.
====== [[Exterior angle property of a Triangle]] ======
==== Concept #: Construction of triangles ====
==== Concept #: Construction of triangles ====
======[[Exploring concurrent lines from given surroundings]]======
======[[Exploring concurrent lines from given surroundings]]======
Interactive activity to introduce concurrent lines using examples from our surroundings.
Interactive activity to introduce concurrent lines using examples from our surroundings.
=====Concept #: Concurrency of medians in triangles.=====
=====Concept #: Concurrency of medians in triangles.=====
Median of a triangle is a line segment from a vertex to the midpoint of the opposite side. A triangle has three medians. Each median divides the triangle into two smaller triangles of equal area. The medians of a triangle are concurrent and the point of concurrence is called the centroid. The centroid is always inside the triangle. The centroid is exactly two-thirds the way along each median. i.e the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex.
Median of a triangle is a line segment from a vertex to the midpoint of the opposite side. A triangle has three medians. Each median divides the triangle into two smaller triangles of equal area. The medians of a triangle are concurrent and the point of concurrence is called the centroid. The centroid is always inside the triangle. The centroid is exactly two-thirds the way along each median. i.e the centroid divides each median into two segments whose lengths are in the ratio 2:1, with the longest one nearest the vertex.
======[[Marking centroid of a triangle|Marking centroid of the triangle]]======
======[[Marking centroid of a triangle|Marking centroid of the triangle]]======
This is a hands on activity to explore concurrent lines formed in a triangle when vertices are joined to the midpoints of the opposite side.
This is a hands on activity to explore concurrent lines formed in a triangle when vertices are joined to the midpoints of the opposite side.
======[[Medians and centroid of a triangle]]======
======[[Medians and centroid of a triangle]]======
The centroid of a triangle is where the three medians intersect. This activity will show you how to find the centroid and you’ll explore several geometric relationships related to centroid and medians.
The centroid of a triangle is where the three medians intersect. This activity will show you how to find the centroid and you’ll explore several geometric relationships related to centroid and medians.
Two objects are similar if they have the same shape, but not necessarily the same size. This means that we can obtain one figure from the other through a process of expansion or contraction, possibly followed by translation, rotation or reflection. If the objects also have the same size, they are congruent. Two triangles are said to be congruent to one another only if their corresponding sides and angles are equal to one another
Two objects are similar if they have the same shape, but not necessarily the same size. This means that we can obtain one figure from the other through a process of expansion or contraction, possibly followed by translation, rotation or reflection. If the objects also have the same size, they are congruent. Two triangles are said to be congruent to one another only if their corresponding sides and angles are equal to one another
==== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] ====
==== Solved problems/ key questions (earlier was hints for problems) ====
=== Projects (can include math lab/ science lab/ language lab)[edit | edit source] ===
===Additional Resources===
==== Resource Title and description ====
1.[http://www.mathopenref.com/tocs/triangletoc.html Triangles]- This resource contain all information related to triangle like definition, types of triangle, perimeter, congruency etc.,
2. [http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.TRIA Triangles]- This helps to know the aplication of geometry in our daily life, it contain videos and interactives.
3. [http://www.mathopenref.com/tocs/congruencetoc.html Congruence]
4. [http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.SHAP&ID2=AB.MATH.JR.SHAP.SIM Similarity and Congruence]
5. The below video gives information about Angle Sum Property by Gireesh K S and Suchetha S S
{{#widget:YouTube|id=GfP8M5GwcdQ}}
====OER====
* Web resources:
** [https://en.wikipedia.org/wiki/Triangle Wikipedia, the free encyclopedia] : The website gives a comprehensive information on triangles from basics to in depth understanding of the topic.
** [https://jsuniltutorial.weebly.com/ix-triangles.html cbsemathstudy.blogspot.com] : The website contains worksheets that can be downloaded. Worksheets for other chapters can also be searched for which are listed based on class.
* Books and journals
* Textbooks
** NCERT Textbooks – [http://ncert.nic.in/textbook/textbook.htm?iemh1=7-15 Class 9]
* Syllabus documents
====Non-OER====
* Web resources:
** [https://www.brighthubeducation.com/middle-school-math-lessons/39674-triangle-properties-and-angles/ Bright hub education] : The website describes a lesson plan for introducing triangles and lists classroom problems at the end of the lesson that can be solved for better understanding.
** [http://www.cpalms.org/Public/PreviewResourceLesson/Preview/40261 CPALMS] : The website contains lesson plan, activities and worksheets associated with triangles.
** [https://www.urbanpro.com/cbse-class-9-maths-construction UrbanPro] : This website gives downloadable worksheets with problems on triangle construction.
** [https://schools.aglasem.com/59755 AglaSem Schools] : This website lists important questions for math constructions.
** [http://www.nios.ac.in/media/documents/SecMathcour/Eng/Chapter-12.pdf National Institute of Open Schooling]: This website has good reference notes on concurrency of lines in a triangle for both students and teachers.
** [http://www.mathopenref.com/ Math Open Reference] : This website gives activities that can be tried and manipulated online for topics on geometry.
* 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 (CBSE, ICSE, IGCSE etc)
=== Projects (can include math lab/ science lab/ language lab) ===
'''''Laboratory Manuals''' - Mathematics : [https://ncert.nic.in/pdf/publication/sciencelaboratorymanuals/classIXtoX/mathematics/lelm402.pdf Click here] to refer activity 15,16,18 and 20'' which explains the properties of Triangle.
=== Assessments - question banks, formative assessment activities and summative assessment activities ===
=== Assessments - question banks, formative assessment activities and summative assessment activities ===
# [[:File:Introducction to Triangles.pdf|Introduction to triangles]]
# [[:File:Types of Triangle by sides.pdf|Types of Triangle by sides]]
# [[:File:Properties of Triangles.pdf|Properties of Triangle]]
[[Category:Class 9]]
[[Category:Class 8]]