# GM5-5: Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.

This means that students will know and apply angle properties relating to intersecting and parallel lines.

The angle properties of lines are:

- Vertically opposite angles are equal, for example a = d, b = c
- Adjacent angles add to 180
^{o, }for example a + b = 180^{o}, a + c = 180^{o} - Corresponding angles are equal, for example a = e, b = f, c = g, d= h
- Interior angles add to 180
^{o}, for example c + e = 180^{o}, d + f = 180^{o} - Alternate angles are equal, c = f, d = e

Students should apply the properties of intersecting and parallel lines to problems like constructing rectangular and skewed picture frames.

Students should find and apply the angle properties of polygons. They may find the formula for the internal angles of regular polygons (equal angles) by measuring and creating a table of results or by reasoning through cutting the polygons into triangles. These angles properties are:

- Interior angles of a polygon with n sides are ((n-2) x 180
^{o})/n. - Exterior angles of any polygon add to 360
^{o}.

## How High? and Other Problems

- Units of Work
- Geometry and Measurement
- Level Five

In this collection of activities we use ruler and compass constructions to draw a variety of shapes and to construct angles such as 90°, 60°, 45° and 15°.

## Ruler and Compass Constructions

- Units of Work
- Geometry and Measurement
- Level Five

In this unit we use rulers and compasses to construct perpendicular lines and to bisect angles. These constructions are used to make a variety of polygons, nets and to illustrate loci.

## Angles, Parallel Lines, and Polygons

- Units of Work
- Geometry and Measurement
- Level Five

In this unit, students will learn to investigate polygons using an instrument of their own construction. They should be able to find the general formula for the number of degrees in any polygon (including a triangle). Finally they will investigate an interesting locus problem related to polygons.

## Flip's flag

- Problem solving activities
- Geometry and Measurement
- Level Five

## Vince's problem

- Problem solving activities
- Geometry and Measurement
- Level Five

Find the centre of a circle using common material or mathematical construction tools.

## Sol's serviettes

- Problem solving activities
- Geometry and Measurement
- Level Five

## Ash in the Air

- Figure It Out activities
- Geometry and Measurement
- Level Five

This is a level 4 and 5 measurement activity from the Figure It Out theme series.

## Pierced polygons

- Rich learning activities
- Geometry and Measurement
- Level Five

The purpose of this multi-level task is to engage students in an investigation applying geometric properties of polygons.

## Inside Irregular Polygons

- Rich learning activities
- Geometry and Measurement
- Level Five

The purpose of this multi-level task is to engage students in using a given rule, to deduce another rule. This is an example of the deductive reasoning required for forming successful geometric proofs.