# Angle sum property

From Karnataka Open Educational Resources

Interior angles of a triangle are in relation and also determine the type of angles that can forms a triangle. This also helps in determining an unknown angle measurement.

## Contents

### Objectives

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

### Estimated Time

### 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 :

### Process (How to do the activity)

Download this geogebra file from this link.

- 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?

Download this geogebra file from this link.

- 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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Download this geogebra file from this link.

- 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}?