Two shapes are similar if the only difference between                          them is their size. Their side lengths are in the same proportions.

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

The object is the starting figure, before a transformation has been applied.

The image is the resulting figure, after a transformation has been applied.

A property of a shape is invariant if that property has not changed after the shape is transformed.

Checking and securing understanding of congruence and similarity

Maths

In this unit, pupils enhanced their understanding of enlargement. In this future unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape. 

In the prior unit, pupils learnt about the different types of transformations. In this unit, pupils' knowledge is extended as negative scale factors are considered as are multiple transformations.

Further transformations

Two shapes are {{ }} if the only difference between them is their size. Their side lengths are in the same proportions. 

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are {{ }}.

Select the transformations that will always produce an image that is congruent to the object.

Andeep: "The shapes are congruent because they have the same angles."

Jacob: "The shapes could be congruent but we need the other sides for shape B."

Laura: "The shapes could be similar but we need the other sides for shape B."

Sam: "Both shapes have the same corresponding side labelled 9 cm."

Sofia: "They have the same angles, but not side lengths so they are similar."

Some Oak pupils discuss whether shapes A and B are congruent or similar. Who is correct?

Shapes A and B are congruent. What is the length of the side marked $$x$$?

Quadrilaterals A and B are similar. The length of the side marked $$x$$ is {{ }} cm.

A property of a shape is __________ if that property has not changed after the shape is transformed.

When an object is transformed the resulting shape is called the {{ }}.

The size of the missing angle in this quadrilateral is {{ }}°.

What are the lengths of the sides that are adjacent to the angle of 80° in this quadrilateral? 

Rectangle B is an enlargement of rectangle A by scale factor 2. Rectangle A has perimeter = 16 cm and area = 15 cm². Both rectangles have integer side lengths. Find the area and perimeter of B.

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