Topic 8: General and Angle Properties of Geometric Figures

By the end of this topic, you will be able to:

1. identify different angles
2. solve problems involving angles at a point on a straight line, angles on transversal and parallel lines
3. identify and use the angle sum of a triangle
4. state and use angle properties of polygons when solving problems polygon reflex supplementary 0 transversal

Keywords

1. acute
2. alternate
3. angle
4. corresponding
5. exterior
6. interior
7. obtuse
8. parallel lines
9. Properties

Introduction

Carpenters use angles to make chairs, tables and sofas. Engineers and Architects use angles to design roads, buildings, sports facilities and many others.

Roof tops form angles as the two roof surfaces slope down from it. Cloth hangers, scissors, pyramids set squares, edge of a table, partly opened doors and many others are examples of angles in real life. Imagine what would happen if angles were not there?

In this topic, you will learn about angle properties of geometric figures and how to apply them in real life situations.

Identifying different angles

Consider the compass on the right.

Turning from W to N clockwise is 90°

Turning from N to S is 180° clockwise or anticlockwise.

Turning anticlockwise from SE to W is 225° (or 135° anticlockwise). You can use things in the environment such as sticks to create and identify angles.

Activity 8.1 Identifying different angles (work in groups)

What you need: sticks, rubber band or threads.

What to do:

3. Tie sticks to form angles of different sizes as you describe them a to their sizes.

Solving Problems Involving Angles at a Point, on a Straight Line, Angles on a Transversal and Parallel Lines.

Angles at a point

In a road junction, what angle does each road make with the other? What happens when two strings are tied at a common point and pulled to different directions? Many angles are created.

Activity 8.2 Identifying angles at a point (work in groups) need:

What you What to do: pen, pencil, notebook, pair of compasses and ruler.

1. Draw two intersecting lines.

2. Identify the angles formed and name them as a, b, c and d.

3. Measure the angles a, b, c, and d at the point.

4. State the sum of the angles in (3) above.

Solving Problems Involving Angles on a Straight Line

From your environment, identify any angles on a straight line. What is the comm feature with those angles?

Activity 8.3 Identifying a straight angle

What you need: a pencil, ruler, pen, protractor

What to do:

1. In groups, draw different lines, vertically, horizontally and diagonally.

2. Mark a point on those lines.

3. Measure the straight angle drawn.

4. Draw a line on the marked point. What angle does it make with the L

5. State the sum of the angle Properties formed on the straight line.

6. Compare your work with other groups’ work.

Solving Problems Involving Transversal and Parallel Lines

A straight road that crosses another straight road as illustrated above, is a good example of transversal parallel lines

Activity 8.4 Solving problems involving angles on transversal and parallel lines (work in groups)

What you need: a ruler, pen, pencil, paper or notebook, protractor

What to do:

Draw horizontal parallel lines AB and PQ and a transversal line MN through them as shown.

1. Measure and record angles marked p to v.

2. Identify which angles are equal and give reason why.

3. State the sum of co-interior angles q and s, r and w.

6. State the total sum of co-exterior angles p and t, u and v.

7. Compare your work with other groups.

Exercise 8.4

Find the missing angles and give a reason for your answer

Knowing and Using Angle Sum of a Triangle

Triangles and Quadrilaterals

When you join three straight sticks, a triangle is formed. Triangles form the basis of many strong structures such as roofs and bridges. How many angles does a triangle have?

Activity 8.5 Knowing and using the angle sum of a triangle

Stating and Using Angle Properties of Polygons when Solving Problems

You can find the angle sum of all interior angles in any polygon by considering the number of triangles within the polygon. In the following activity, you will use triangles to find the interior and exterior angle sums of a polygon.

Activity 8.6 Stating and using angle properties of Polygons when solving problems

What you need: notebook, geometry set

Precaution: Be careful with sharp geometric instruments not to injure yourself. What to do: Draw regular polygons of your choice like the ones below.

1. Measure and find the sum of all a) interior angles a) exterior angles

2. Form triangles from the polygon:

3. How many triangles are in the polygon?

4. Compare the interior angle sum with the number of triangles formed.

5. Compare the number of sides, with the number of triangles.

6. State the formula you can use to find the interior angle sum of a polygon

7. Now compare the number of sides, exterior angle sum and the exterior angle.

8. State the formula for finding the exterior angle of a polygon.

9. Use your findings to complete the table below.

10. Present your work to the whole class.

Example

a) The interior angle of a polygon is 120°. Name the polygon.

b) What is the interior angle sum of the polygon?

Exercise 8.6

1. The interior angle of a regular polygon is 140°.

a) How many sides has the polygon?

b) Calculate its interior angle sum.

2. The interior angle sum of a regular polygon is 900°.

a) Name the polygon.

b) What is the size of each exterior and interior angle?

3. The interior angle of a regular polygon is 108° more than its exterior angle.

a) What is the size of each exterior and interior angle Properties?

b) Calculate the interior angle sum of the polygon.