Triangles

Additional Resources

OER

1. List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
2. Books and journals
3. Textbooks
4. Syllabus documents

Non-OER

1. List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both
2. Books and journals
3. Textbooks
4. Syllabus documents

Learning Objectives

Concept #1. Formation of a triangle, elements of a triangle and its measures

1. A triangle is a three sided closed figure.
2. It is one of the basic shapes in geometry.
3. It triangle is a polygon with three edges and three vertices.
4. There are three angles in a triangle formed at the three vertices of the triangle.
5. Interior and exterior angles in a triangle at a vertex, together form a linear pair.

Activity No # 1 : Formation of a triangle

Formation of a triangle

• Objectives

1. Understand formation of triangles
2. Recognize elements of triangle
3. Introduce concepts of exterior angle.

• Pre-requisites

Prior knowledge of point, lines, angles, parallel linesResources needed

• Resources needed

1. Digital : Computer, geogebra application, projector.
2. Non digital : Worksheet and pencil
3. Geogebra files : “1.Introduction to a triangle.ggb”

• How to do

1. Use the geogebra file to illustrate.
2. How many lines are there? Are the lines meeting?
3. Are the two lines parallel? How can you say they are parallel or not?
4. How many angles are formed at the point of intersection?
5. What is the measure of the total angle at the point of intersection of two lines?
6. Of the four angles formed which of the angles are equal? What are they called?
7. Do the three intersecting lines enclose a space? How does it look? It is called a triangle.
8. What are the points of intersection of these three lines called?
9. The line segments forming the triangle are called sides.
10. How many angles are formed when three lines intersect with each other?
11. How many angles are enclosed by the triangle?

• Evaluation at the end of the activity

1. Can there be a closed figure with less than three sides?
2. Can the vertices of the triangle be anywhere on a plane?
3. What will happen if the three vertices are collinear?

Activity No # 2 : Elements of a Triangle

• Objectives

1. To understand the elements of a triangle

• Pre-requisites

Prior knowledge of point, lines, angles, parallel lines

• Resources needed

1. Digital : Computer, geogebra application, projector.
2. Non digital : Worksheet and pencil,6-8 strings (preferably in different colours)
3. Geogebra files : “2. Elements of a triangle.ggb”

• How to do

1. Students work individually but in their groups.
2. Take the strings and place them in such a way as to make a closed figure.
3. What is the smallest number of strings with which you can form a closed figure?
4. What is this figure called?
5. Can you just draw the lines along the strings and see what you get?
6. When you drew, what did you draw?  (Was it a line or was it an angle or was it a line segment?). It is a lime segment – how many line segments are there?
7. When two line segments joined, what is it called?  (A vertex). How many vertices are there?
8. Is there any angle formed when you made this figure? How many angles were formed?
9. Show a simple Geogebra file with triangles – Use this file to demonstrate that every triangle has the elements - vertices, sides and angles
10. How many triangles were formed?  Were there any strings left over?
11. For each of the triangles trace the shape on the book and write down the elements of the triangle in the following format {| class="wikitable" ! ! ! ! |- | | | | |- | | | | |- | | | | |}
12. For each of the triangles observe (inspect visually) which is the longest side and which is the shortest side {| class="wikitable" !Triangle name !Largest angle !Largest side !Smallest angle !Smallest side |- | | | | | |- | | | | | |- | | | | | |}
13. Allow the students to explore if there is any connection between the two?
14. After the students see the Geogebra file, they can attempt an alternative worksheet like below: {| class="wikitable" !Side 1 !Angle 1 (opposite angle) !Side 2 !Angle 2 (opposite angle) !Side 3 !Angle 3 (opposite angle) !Largest side and angle ex-side1,angle1 !Smallest side and angle ex-side3,angle3 |- | | | | | | | | |- | | | | | | | | |- | | | | | |}

Evaluation at the end of the activity

1. Have the students been able to identify the elements in a triangle?

2. Have they been able to extrapolate any connection between the angle and side in a triangle?