Angle sum property

The angle sum property of a triangle states that the angles of a triangle always add up to 180°. Every triangle has three angles and whether it is an acute, obtuse, or right triangle, the angles sum to 180°

Objectives

• To establish the angle sum property of a triangle
• To help visualization of the geometric proof

Prerequisites/Instructions, prior preparations, if any

Prior understanding of point, lines and angles, adjacent angles, vertically opposite angles, linear pair, parallel lines, alternate angles, corresponding angles.

Materials/ Resources needed

• Digital : Computer, geogebra application, projector.
• Non digital : Worksheet and pencil.
• Geogebra files :
  1. “a. Angles in a right triangle.ggb” ,
  2. “b. Angle sum property proof.ggb” ,
  3. “c. Angle sum property of a triangle.ggb”

Process (How to do the activity)

• Use the file - “a.Angles in a right triangle.ggb”
• Ask students what is the kind of triangle they observe.
• Draw a parallel line to the side containing the right angle through the opposite vertex by dragging point D along the x-axis
• Students should be able to recognize the corresponding angles formed when the parallel line is drawn.
• Students should be able to recognize the alternate angles formed. Is the alternate angle same as one of the angles of the triangle.
• So what can you say about the all the angles of the triangle?
• With the file - “b. Angle sum property proof.ggb”
• Draw a line perpendicular to a side passing through the opposite vertex. How many triangles are formed. What kinds of triangles are formed?
• In each of the two triangles if on angle is 90^o, what will be the sum of the other two angles. What is the sum of these angles?
• Children can record the values of the angles of a triangle in the worksheet

Observation	Angle 1	Angle 2	Angle 3	Angle 1 + Angle 2 + Angle 3	What can you say about sum of angles?
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.
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• With the file – “c. Angle sum property of a triangle.ggb”
• Ask students what happens when the three angles of the triangle are placed adjacent to each other.
• What can you say about the line drawn?
• Is it parallel to one of the sides?
• What can you say about the pairs of angles – look at the matching colors.
• Once the parallel line reaches the vertex, how many angles are formed?
• Students should be able to identify the two angles moving are corresponding angles as the line moving is parallel to one of the sides.
• Students can see that when the three angles of the triangle are placed adjacent to each other they form a straight line.

Evaluation at the end of the activity

• Have students able to conclude if the sum of angles in any triangle is 180^o?