**"Geometric proof"**

## Years 8 – 12 Tri-Fold

*By toni On 15 May, 2020 · Leave a Comment*

Take any triangle and label it ABC with A as the largest angle. Fold the triangle along PQ, PS and QT where the points P and Q are the midpoints of AB and AC and PS and PT are perpendicular to BC.

What do you notice? Why does this happen? Will it […]

## Years 10 – 11: Investigating circle theorems

*By Barrie Barnard On 9 September, 2019 · Leave a Comment*

Activity 1: Finding the centre of the circle

You will need a cut-out paper circle (about 12cm diameter).

Use a circle that does not show the centre. Fold your circle along a diameter. Mark the ends A and B. Now unfold your circle and then fold again along a different diameter and mark the […]

## Years 11 – 12 Encircling

*By toni On 15 July, 2017 · Leave a Comment*

This shape is an equilateral triangle sitting on top of a square.

What is the radius of the circle that circumscribes the shape?

Click here for a hint if you need one to get started.

Click here for the Notes for Teachers.

This problem is adapted from the […]

## Grade 12 Pythagoras Similarly

*By toni On 25 July, 2016 · Leave a Comment*

There are hundreds of proofs of Pythagoras Theorem.

This diagram shows a proof.

Look carefully. Can you see three squares?

Assuming that they are squares, can you prove that four of the triangles are congruent?

Can you explain the proof?

The second diagram shows a well known proof using similar triangles.

## Grades 10 to 12 Three By One

*By toni On 1 June, 2016 · 2 Comments*

This rectangle measures three units by one unit.

The diagram shows three angles a, b and c.

How many ways can you prove that a + b = c?

What other interesting properties can you find?

When this activity was originally published on NRICH, two boys from Madras School in St Andrew’s, Scotland sent […]

## Years 10 – 12 Geoprob

*By toni On 29 March, 2016 · Leave a Comment*

The point E is inside the square ABCD and AEB is an equilateral triangle. Find the angles EBC, BEC and ECD and give reasons for your answers.

Click for Teacher-Notes-GEO-PROB.

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