1. Home

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

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Elaboration on this Achievement Objective

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

The angle properties of lines are:

  1. Vertically opposite angles are equal, for example a = d, b = c
  2. Adjacent angles add to 180o, for example a + b = 180o, a + c = 180o
  3. Corresponding angles are equal, for example a = e, b = f, c = g, d= h
  4. Interior angles add to 180o, for example c + e = 180o, d + f = 180o
  5. Alternate angles are equal, c = f, d = e

angle properties image.

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:

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

 

 

Teaching resources for this Achievement Objective
Resource logo

Angles, Parallel Lines, and Polygons

Level Five
Geometry and Measurement
Units of Work
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.
  • Make an instrument to measure turning in a range of situations.
  • Measure angles using the new instrument.
  • Investigate angles of polygons.
  • Find counter-examples to incorrect conjectures.
Resource logo

Ash in the Air

Level Five
Geometry and Measurement
Figure It Out activities
This is a level 4 and 5 measurement activity from the Figure It Out theme series. A PDF of the student activity is included.

find the area of an ellipse

interpret data on chart

Resource logo

Flip's flag

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Apply the angle properties of squares, rectangles and triangles.
  • Use fractions to express the relationships between the areas of rectangles, squares and triangles.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic).
Resource logo

How High? and Other Problems

Level Five
Geometry and Measurement
Units of Work
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°.
  • Apply Pythagoras' theorem.
  • Use their knowledge of the sum of interior angles of a polygon.
  • Construct angles based on halving and combining 90° and other straightforward angles.
  • Apply knowledge of length and area.
Resource logo

Inside Irregular Polygons

Level Five
Geometry and Measurement
Rich learning activities
The purpose of this activity 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.
Resource logo

Never get lost

Level Five
Geometry and Measurement
This extended, cross curricular unit supports students to learn and apply theories around scale, bearings and compass directions in a context that enhances their engagement and produces an authentic and useful outcome.
Resource logo

Pierced polygons

Level Five
Geometry and Measurement
Rich learning activities
The purpose of this activity is to engage students in an investigation applying geometric properties of polygons.
Resource logo

Ruler and Compass Constructions

Level Five
Geometry and Measurement
Units of Work
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.
  • Construct perpendicular bisectors of lines.
  • Construct bisectors of angles.
  • Use these skills to construct equilateral triangles and squares with a given side length, parallel lines, parallelograms and trapeziums, and regular polygons with a small number of sides.
  • Use construction techniques300
Resource logo

Sol's serviettes

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Use the areas of triangles and squares to find unknown lengths.
  • Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).
Resource logo

Synchronised Swim Shapes

Level Five
Geometry and Measurement
The purpose of this unit is to engage students in applying their understanding of geometric thinking to design and describe formations and the translations and/or rotations needed to create those formations. This is explored in the context of choreographing a synchronised swimming routine and...
  • Find the size of angles. 
  • Describe the features of regular polygons, including the size of their interior angles. 
  • Apply knowledge of angles, quadrilaterals, and regular polygons to problem solving contexts.
Resource logo

Vince's problem

Level Five
Geometry and Measurement
Problem solving activities
This problem solving activity has a geometry focus.
  • Find the centre of a circle using common material or mathematical construction tools.