Difference between revisions of "Triangles"
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* Web resources: | * 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://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 | + | ** [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 | * Books and journals | ||
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* Web resources: | * 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. | ** [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 | + | ** [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 | + | ** [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. | ** [https://schools.aglasem.com/59755 AglaSem Schools] : This website lists important questions for math constructions. | ||
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===Learning Objectives=== | ===Learning Objectives=== | ||
* Identifying a triangle and understanding its formation | * Identifying a triangle and understanding its formation | ||
| − | * Recognizing | + | * Recognizing parameters related to triangles |
| − | * Understanding formation of triangles based on sides and angles | + | * Understanding different formation of triangles based on sides and angles |
* Establishing relationship between parameters associated with triangles | * Establishing relationship between parameters associated with triangles | ||
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==== Concept 1: Formation of a triangle, elements of a triangle and its measures ==== | ==== Concept 1: Formation of a triangle, elements of a triangle and its measures ==== | ||
| − | + | The triangle is the basic geometrical figure that allows us to best study geometrical shapes. A quadrilateral can be partitioned into two triangles, a pentagon into three triangles, a hexagon into four triangles, and so on.These partitions allow us to study the characteristics of these figures. And so it is with Euclidean geometry—the triangle is one of the very basic parts on which most other figures depend. Here we will be investigating triangles and related its properties | |
===== Activities ===== | ===== Activities ===== | ||
====== [[Formation of a triangle]] ====== | ====== [[Formation of a triangle]] ====== | ||
| − | + | Introducing formation of a shape with least number of lines and the space enclosed by these lines form a geometric shape.The key geometric concepts that are related with this are explained. | |
====== [[Measures in triangle|Elements and measures in triangle]] ====== | ====== [[Measures in triangle|Elements and measures in triangle]] ====== | ||
| − | + | The components that make a triangle are investigated. Measuring these components gives a better understanding of properties of triangles. Relation between these components are conceptualized. | |
====== [[Interior and exterior angles in triangle]] ====== | ====== [[Interior and exterior angles in triangle]] ====== | ||
| Line 69: | Line 69: | ||
====== [[Relation between interior and exterior angles in triangle|Exterior angle theorem]] ====== | ====== [[Relation between interior and exterior angles in triangle|Exterior angle theorem]] ====== | ||
| − | Relation between angles formed inside a triangles and angles outside a triangle | + | Relation between angles formed inside a triangles and angles outside a triangle. Exterior and interior angles and their dependencies |
==== Concept 4: Construction of triangles ==== | ==== Concept 4: Construction of triangles ==== | ||
Revision as of 11:27, 25 April 2019
Concept Map
Additional Resources
OER
- Web resources:
- Wikipedia, the free encyclopedia : The website gives a comprehensive information on triangles from basics to in depth understanding of the topic.
- 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 – Class 9
- Syllabus documents
Non-OER
- Web resources:
- 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.
- CPALMS : The website contains lesson plan, activities and worksheets associated with triangles.
- UrbanPro : This website gives downloadable worksheets with problems on triangle construction.
- AglaSem Schools : This website lists important questions for math constructions.
- Books and journals
- Textbooks:
- Syllabus documents (CBSE, ICSE, IGCSE etc)
Learning Objectives
- Identifying a triangle and understanding its formation
- Recognizing parameters related to triangles
- Understanding different formation of triangles based on sides and angles
- Establishing relationship between parameters associated with triangles
Teaching Outlines
Concept 1: Formation of a triangle, elements of a triangle and its measures
The triangle is the basic geometrical figure that allows us to best study geometrical shapes. A quadrilateral can be partitioned into two triangles, a pentagon into three triangles, a hexagon into four triangles, and so on.These partitions allow us to study the characteristics of these figures. And so it is with Euclidean geometry—the triangle is one of the very basic parts on which most other figures depend. Here we will be investigating triangles and related its properties
Activities
Formation of a triangle
Introducing formation of a shape with least number of lines and the space enclosed by these lines form a geometric shape.The key geometric concepts that are related with this are explained.
Elements and measures in triangle
The components that make a triangle are investigated. Measuring these components gives a better understanding of properties of triangles. Relation between these components are conceptualized.
Interior and exterior angles in triangle
Angles that are formed when a triangle is formed.
Concept 2: Types of triangles based on sides and angles
Triangles can be based on its elements such as sides and angles. Students are able to recognize these formations.
Activities
Types of triangles based on sides
Formation of a triangle depends on measures of sides.
Types of triangles based on angles
Formation of a triangle depends on measures of angles.
Concept 3: Theorems and properties
Properties of triangles are logically proved by deductive method. Relations ships between angles of a triangle when a triangle is formed are recognized and understood.
Activities
Angle sum property
Relation between angles formed inside a triangle
Exterior angle theorem
Relation between angles formed inside a triangles and angles outside a triangle. Exterior and interior angles and their dependencies
Concept 4: Construction of triangles
Constructing geometric shapes to precision using a scale and a compass helps in understanding of properties of the shape. Constructing geometric shapes with minimum number of parameters enhances thinking skills.
The following constructions are based on three essential parameters that are required for construction following the SSS, SAS and ASA theorems
Activities
Construction of a triangle with three sides
Construction of a triangle based on the SSS congruence rule
Construction of a triangle with two sides and an angle
Construction of a triangle based on SAS congruence rule
Construction of a triangle with two angles and included side
Construction of a triangle based on ASA congruence rule
Construction of a right angled triangle
Construction of a triangle based on RH congruence rule
Construction of a triangle with perimeter and base angles
Construction on a triangle with give parameters using SAS congruence rule
Construction of a triangle with a side, an angle and sum of two sides
Construction on a triangle with give parameters using SAS congruence rule
Construction of a triangle with a side, an angle and difference to two sides
Construction on a triangle with give parameters using SAS congruence rule