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

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

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

Scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

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

Checking understanding of similarity

Maths

Checking understanding of congruence

Similarity in shapes

Congruence in shapes

Congruent, similar or neither

Rotational symmetry

Congruent triangles (SSS)

Congruent triangles (SAS)

Congruent triangles (ASA and AAS)

Congruent triangles (RHS)

Applying the criteria for congruence

Demonstrating Pythagoras' theorem

Further demonstrating of Pythagoras' theorem

Length of the hypotenuse

Length of a shorter side

Determining which side

Pythagoras' theorem in context

Problem solving with similarity and Pythagoras' theorem

In this unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In the future unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In the prior unit, pupils explored the effects of different transformations and whether the transformed shape was congruent or similar to the original shape. This is built on in this unit where pupils formalise the criteria for determining congruence in triangles and study rotational symmetry.

This unit explores the concepts of congruence and similarity, and ways to prove or disprove similarity between shapes. We then explore further properties of triangles with Pythagoras' Theorem.

Geometrical properties: similarity and Pythagoras' theorem

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

Co-interior angles are on the same side of the transversal line and in between the two other lines.

Rotational symmetry describes when a shape appears the same after some rotation. The order of rotational symmetry is the number of times the image appears the same as the object in one full turn.

The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).

A hypotenuse is the side of the right-angled triangle which is opposite the right-angle.

A right-angled triangle has exactly one 90° interior angle.

A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.

The perpendicular height is the perpendicular distance from the base to the opposite vertex.

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

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Geometrical properties: similarity and Pythagoras' theorem

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