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 :
 * “a. Angles in a right triangle.ggb” ,
 * “b. Angle sum property proof.ggb” ,
 * “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 90o, 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

Evaluation at the end of the activity
 * 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.
 * Have students able to conclude if the sum of angles in any triangle is  180o?