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- Enlarge a shape by a positive integer scale factor (review)
- Enlarge a shape by a fractional scale factor (review)
- Identify similar shapes
- Work out missing sides and angles in a pair given similar shapes (review)
- Use parallel line rules to work out missing angles
- Establish a pair of triangles are similar
- Understand the difference between congruence and similarity
- Understand and use conditions for congruent triangles

For higher-attaining pupils:

- Enlarge a shape by a negative scale factor
- Explore areas of similar shapes
- Explore volumes of similar shapes
- Solve mixed problems involving similar shapes
- Prove a pair of triangles are congruent

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Transformations Video A demonstration of the four basic transformations: reflection, translation, rotation and enlargement.
- Angle Parallels Understand and use the relationship between parallel lines and alternate and corresponding angles.
- Angle Chase Find all of the angles on the geometrical diagrams.
- Angle Theorems Diagrams of the angle theorems with interactive examples.
- Construct a congruent triangle Construction (with compass and straight edge) of a triangle congruent to a given triangle.
- Transformations Draw transformations online and have them instantly checked. Includes reflections, translations, rotations and enlargements.
- Congruent Triangles Video Learn the conditions for two triangles to be congruent and then use this information to solve problems.
- Congruent Triangles Test your understanding of the criteria for congruence of triangles with this self-marking quiz.
- Scale Factors Video The scale factor, area factor and volume factor of similar shapes are quite different.
- Similar Shapes Questions about the scale factors of lengths, areas and volumes of similar shapes.
- Negative Enlargement A video from MathsWatch about Enlargement by a Negative Scale Factor.
- Blow Up Click on all the points that could be the centre of enlargement of the shape if the image does not go off the grid.
- Congruent Parts Use the colours to dissect the outlines into congruent parts.
- Similar Parts Use the colours to dissect the outlines into similar parts.

Here are some exam-style questions on this topic:

- "
*A triangle, ABC, is drawn (not to scale) with AC = 12.6 cm.*" ... more - "
*(a) Victor estimates the height of a flag pole by holding a ruler vertically so the height of the flag pole is exactly covered by the ruler when he is standing 240 centimetres from the flag pole.*" ... more - "
*Prove that triangle ABC is congruent to triangle CDA if ABCD is a parallelogram.*" ... more - "
*The design below is made from six congruent trapezia and two red triangles.*" ... more - "
*The diagram below shows two parallel lines, AB and CD, crossed by a transversal line EF. Find the values of \(w\), \(x\) and \(y\).*" ... more - "
*In the following diagram AD is parallel to CE and AD = CD. Angle AFD is a right angle.*" ... more - "
*ABCD is a parallelogram with diagonals meeting at E. Prove that triangle ABE is congruent to triangle CDE.*" ... more - "
*Triangle JKL is the cross-section of a prism of length 25cm.*" ... more - "
*The following points have been plotted then joined up in order to make an irregular hexagon.*" ... more - "
*The circumference of the red circle is 80% of the circumference of the blue circle.*" ... more - "
*Describe fully the single transformation that maps trapezium A onto trapezium B.*" ... more - "
*Shape ABCD is a trapezium. It is an enlargement of the smaller blue trapezium with a negative scale factor, \(k\).*" ... more - "
*(a) Find the area of a regular octagon if the distance from its centre to any vertex is 10cm.*" ... more - "
*The three boxes pictured below are mathematically similar.*" ... more - "
*ABC is an isosceles triangle in which AB = AC.*" ... more - "
*Two similar pentagonal based pyramids have surface areas 200 cm*" ... more^{2}and 50 cm^{2}respectively.

Here are some Advanced Starters on this statement:

**Square in Rectangle**

Find the area of a square drawn under the diagonal of a rectangle more**Three Right Triangles**

Calculate the lengths of the unlabelled sides of these right-angled triangles. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

- Angles Pupils should understand that angles represent an amount of turning and be able to estimate the size of angle. When constructing models and drawing pupils should be able to measure and draw angles to the nearest degree and use appropriate language associated with angles. Pupils should know the angle sums of polygons and that of angles at a point and on a straight line. They will learn about angles made in circles by chords, radii and tangents and recognise the relationships between them. Pupils will work with angles using trigonometry, transformations and bearings. In exams pupils are often instructed that while non-exact answers should be given to three significant figures, angle answers should be given to one decimal place.
- Bearings A bearing is a description of a direction. It is the number of degrees measured in a clockwise direction from north as seen from above. Convention, probably born out of the need to be quite clear when saying a bearing over a crackly aircraft radio or storm at sea, three figures are given for each bearing. So 90 degrees would be expressed as 090 degrees. The four main directions are known as the cardinal points. These are north (360°), east (090°), south (180°) and west (270°). The directions in between those are known as the half cardinal points and can be expressed as north-east (045°), south-east (135°), south-west (225°) and north west (315°). The study of bearings in Mathematics provides a practical, real-life application of angles and geometry. It can provide a need for numerical calculations, scale drawing and estimation.
- Construction In a way this topic is quite different to all of the other topics in school mathematics. It requires a practical skill as well as the understanding of the geometrical concepts. It also requires a sharp pencil, a sturdy ruler and a decent pair of compasses. Younger children should practise using the drawing instruments to make patterns. They will then progress to constructing accurate diagrams, plans and maps. Older pupils are taught to derive and use the standard ruler and compass constructions for the perpendicular bisector of a line segment, the perpendicular to a given line from a given point and the bisector of a given angle.
- Enlargements When areas and volumes are enlarged the results are far from intuitive. Doubling the dimensions of a rectangle produces a similar shape with four times the area! Doubling the dimensions of a cuboid produces a similar shape with eight times the volume! The activities provided are intended to give pupils experiences of dealing with enlargements so that they better understand the concept and are able to produce diagrams, make models and answer questions on this subject. Once positive integer scale factors have been mastered the notion of fractional and negative scale factors await discovery!
- Shape This topic is aimed at the learners of basic geometry, which is the study of size, shape and position. More than other areas of mathematics this topic helps pupils to learn about the definitions and properties of basic shapes. There are many activities provided ranging from simple shape naming games to applying more advanced formulas and theorems. The most popular activities however are those involving pupils to count the number of triangles or rectangles in patterns and come up with effective strategies and justifications for their answers. The work pupils produce for this topic can make very good display material. The use of colour can enhance the diagrams and make the learning environment more conducive to study. There are many connections between the mathematics of shape and Art. There are fascinating works of art based on symmetry, tessellations and transformations.
- Transformations A transformation in mathematics is an operation performed on a shape (or points) which changes the view of that shape (or points). This topic includes four transformations namely reflection, translation, rotations and enlargement. A reflection can best be described as the mirror image of a shape in a given line (which acts as the mirror). After reflection the shape remains the same size but the orientation is the mirror image of the original. The transformation known as a translation can be thought of as a movement or shift in position. The size and orientation of the shape remains the same but the position on the plane changes. A rotation can be described as turning. This transformation is defined by the angle of turning and the centre of rotation (the point which does not move during the turning). Finally enlargement is the term we use when a shape increases in size but maintains the same shape. The shape after enlargement is defines as being similar to the shape before enlargement. His use of the word similar has a precise mathematical meaning. All of the angles in the enlarged shape are the same as the angles in the original shape and the lengths of the sides are in the same proportion. An enlargement is defines by the scale factor of the enlargement and the centre of enlargement. We use the term enlargement even if the shape becomes smaller (a scale factor between minus one and one). A negative scale factor will produce an enlarged mirror image of the original shape.

Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.

You have four minutes to write down as many equations as you can involving B, T and S.

The blue point is exactly in the middle of two red points. What are their coordinates?

If the dimensions of an object double, its volume increases by a factor of eight.

Estimate the size of an alien given the size of their hand. This could be an introduction to scale factors.

The missing square puzzle is an optical illusion used to help students reason about geometrical figures.

It is called Refreshing Revision because every time you refresh the page you get different revision questions.

Find a word whose letters would cost exactly ninety nine pence.

How many times can you take one number from another?

Six is a perfect number as it is the sum of its factors. Can you find any other perfect numbers?

Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.