Triangles

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Concept Map

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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
  • 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

Concept 5: Concurrency in triangles