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These are the Transum resources related to the statement: "Pupils should be taught to identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

- 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.
- Congruent Triangles Test your understanding of the criteria for congruence of triangles with this self-marking quiz.
- Congruent Triangles Video Learn the conditions for two triangles to be congruent and then use this information to solve problems.
- Construct a congruent triangle Construction (with compass and straight edge) of a triangle congruent to a given triangle.
- Scale Factors Video The scale factor, area factor and volume factor of similar shapes are quite different.
- Similar Parts Use the colours to dissect the outlines into similar parts.
- Similar Shapes Questions about the scale factors of lengths, areas and volumes of similar shapes.
- Transformations Draw transformations online and have them instantly checked. Includes reflections, translations, rotations and enlargements.
- Transformations Video A demonstration of the four basic transformations: reflection, translation, rotation and enlargement.

Here are some exam-style questions on this statement:

- "
*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 - "
*ABCD is a parallelogram with diagonals meeting at E. Prove that triangle ABE is congruent to triangle CDE.*" ... more - "
*ABC is an isosceles triangle in which AB = AC.*" ... more

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

- 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 volume! 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 scale factors have been mastered the notion of fractional and negative scale factors await discovery!
- 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.
- 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.

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