**"Theorem of Pythagoras"**

## Grades 8 to 12 A Mathematical Lens

*By toni On 2 July, 2019 · Leave a Comment*

STEP 1

1a) Double click on the picture above to start the movie showing how to draw a circle using the paperclip compass.

1b) Draw 2 circles of the same radius with centres A and B so that each circle goes through the centre of the other […]

## Grades 9 to 12 Pyramids in a Cube

*By toni On 29 June, 2019 · Leave a Comment*

To make a model showing how cubes are made up of three square based pyramids, you will need a cardboard box, some string, some colouring pens and a knife or scissors to cut the box.

From one corner of a box cut squares all exactly the same size to form 3 faces of a […]

## Grades 8 to 12 Cuboids and roots

*By toni On 29 June, 2019 · Leave a Comment*

Copy this diagram. To draw a cube first draw a square, then draw another square the same size that looks as if it is behind the first square, then join the vertices with four parallel lines.

Why do the diagonals of a unit cube have lengths √2 and √3?

What are the lengths of the […]

## Grades 11 and 12 Kite

*By toni On 27 July, 2018 · Leave a Comment*

Take a sheet of A4 paper. First fold the top left corner to meet the bottom edge and press the fold flat. Then fold the top right corner to meet the edge that you folded down.

Can you prove that the quadrilateral you have made is a kite?

Can you find the perimeter of the […]

## UPPER SECONDARY G2 PYTHAGORAS THEOREM AND SIMILARITY

*By toni On 5 January, 2018 · 2 Comments*

Investigating proofs of Pythagoras Theorem by similar triangles and practical jig-saw methods. Extension to the Cosine Rule.

Click here to download a pdf with all you need to run your own professional development workshop.

## Grades 11 and 12 Degree Ceremony

*By toni On 19 July, 2017 · Leave a Comment*

Draw a triangle with angles x, (45 + x) and (45 – x) degrees.

What does Pythagoras Theorem tell you about these angles?

Use this information to find this sum of squares of sines:

See the AIMSSEC Notes for Teachers.

This problem is adapted from the NRICH task Degree […]

## Grades 8 to 10 GRAPHICAL TRIANGLE

*By toni On 16 November, 2016 · Leave a Comment*

What is the area, (in square units) of the triangle formed by the three lines whose equations are: y − x = 6, x − 2y = 3 and x + y = 6?

This problem is adapted from the NRICH task Graphical Triangle with permission […]

## Grades 8 to 10 Riding on Pythagoras 1

*By toni On 3 November, 2016 · Leave a Comment*

1. Find the area of the quadrilateral.

2. The rectangle is cut into two pieces along the dotted line and rearranged to make a triangle. Find the perimeter of the triangle.

## Grades 8 to 10 Riding on Pythagoras 2

*By toni On 3 November, 2016 · Leave a Comment*

The diagram shows a septagon ABCDEFG in which the lengths GA, AB, BC, CD, DE, EF are all equal and FG = 6 units. The area of the square BDFG is half the area of the septagon. Find the perimeter of the septagon.

## Grades 8 to 12 Pythagoras Jigsaw

*By toni On 11 August, 2016 · Leave a Comment*

The right angled triangles numbered 1, 2, 3 and 4 in the diagrams all have sides of length a, b and c. They are identical (congruent) copies of each other.

Cut 4 congruent right angled triangles from some scrap paper. Arrange them as shown in diagram […]

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