**"Angles"**

## Grades 7 to 10 Constructing circle and line patterns

*By toni On 18 February, 2018 · Leave a Comment*

The picture shows you how to use a paper clip to draw circles. You just need to open out the paper clip as shown,

Draw a circle and mark 24 points equally spaced around the circumference. To do this, draw a circle and mark the centre, and mark your first point on […]

## Grades 4 to 9 COMMAND THE ROBOT 1

*By toni On 20 November, 2017 · Leave a Comment*

What do you know about robots? What are drones? Are driver-less cars actually robots? What do you think about robots that move around warehouses to pick up and carry loads from place to place, about robots that mow lawns and clean floors and about robots that control complicated machinery in factories?

## Grades 11 & 12 Why the same?

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

In the diagram ASRC and BCQP are squares and PU and ST are perpendicular to the straight line TABU.

Prove that PU + ST = AB.

## Grades 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 […]

## Grades 7 to 9 Ratty

*By toni On 22 November, 2016 · Leave a Comment*

If you know the sizes of the angles marked with coloured dots in the diagram which angles can you find by calculation? Explain your reasoning.

If you also know that AB and CD are parallel which angles can you find?

What extra information do you need to find all the numbered angles?

[…]

## Grades 8 to 12 Tri-Fold

*By toni On 13 September, 2016 · 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 […]

## Grades 7 to 9 Angle Sum

*By toni On 8 September, 2016 · Leave a Comment*

For any triangle you can construct a line through one of the vertices parallel to the opposite edge.

Using what you know about angles and parallel lines prove that the angles of the triangle add up to 180 degrees.

## Grades 10 to 12 Trig Lengths

*By toni On 23 July, 2016 · Leave a Comment*

In the diagram the line OS is perpendicular to the lines OR and PQ.

The line RS is a tangent at P to the circle centre O and radius 1 unit.

Find the lengths OQ, PQ, PS, OS, OR and RP.

If OS and OR lie on the coordinate axes, what are the coordinates […]

## Grades 10 to 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.

## Grades 7 to 12 Tessellating Quadrilaterals

*By toni On 23 June, 2015 · Leave a Comment*

We say that a shape tessellates if we can fit together copies of it to cover a flat surface without leaving any gaps and this covering can be extended in all directions.

The question here is “What can we find out about tessellating different quadrilaterals?”

It’s quite easy to see how […]

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