Circle Theorems

Play around with these so that you become familiar with the different shapes and patterns.

Interactive animations on circle theorems and corollaries.

Four things to know about angles and circles.

1. The angle at the centre is twice the angle on the circle that marks out the same arc - the diagram below shows different examples of this.

2. Angles  standing on the same arc are equal.

3. The angle in a semi-circle is a right angle (the angle on a diameter is a right angle).

4. The sum of the opposite angles in a cyclic quadrilateral is 180.

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Length and Area

Rectangles, Parallelograms and Triangles
You should know how to calculate the area of each shape.
You can go through five animations here.

Circles
See here.

Remember there is useful information in your tables, see pages 8,9 and 10. Click on each page to see a larger view.

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Geometry Word Search Solution

Constructions - Introduction

When you see the word "construction" in a question this means that 

• you should draw an accurate and neat diagram
• use a compass, ruler etc
• use a sharp pencil (a normal pencil e.g. HB)
• show "construction marks" e.g. if you drew arcs with a compass you should not rub these out when you are finished.

You will find step by step instructions for all the first year constructions here.


Second years need to be able to construct the triangles given - SSS, SAS, ASA or RHS
See chapter 25

Doing lots of constructions helps you when you move onto tackling problems in geometry.

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1st Year Geometry

When two lines intersect the vertically opposite angles are always equal. 
Can you explain why this has to be true? 
Hint: the sum of the angles in a straight angle is 180˚. 

The angle animations are here here and two of them show vertically opposite angles.

There are more animations here for you to explore.

Word Search for Geometry
Solutions here.
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1st Year Constructions

Below are excellent demonstrations on most of the constructions - well worth a look. Just concentrate on being able to do each construction. Each pagealso has a lot of extra information explaining why the constructions work but it is probably a bit advanced for first year.

The links to individual pages are listed below.

• Bisect an Angle Active Maths 1 p.184
• Perpendicular Bisector a Line Segment Active Maths 1 p.186
• Perpendicular to a line through a point on the line using a compass. Active Maths 1 p.188
• Parallel to a line through a given point using a compass. Active Maths 1 p.191
• Line segment of a given length. This construction is mainly used to copy a line segment without measuring it. Active Maths 1 p.195-6
• Construct a given angle - this is just using your protractor!
• Divide a Line Segment into Three or More Equal Segments there is an animation here. The video below shows you how to do this construction. The original PowerPoint is much clearer and can be downloaded here (requires PowerPoint 2010 or later). Active Maths 1 p.194

• This video shows you a quick way to draw parallel lines using a set square. 

Parallel Line and Set Square by Green Maths

The first five animations come from this website

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