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# Big ideas

When students are able to build new ideas on sound foundational concepts, a deeper understanding of geometry is developed. You can help your students to make vital connections between ideas and to develop reasoning skills by scaffolding their experiences of geometric relationships.

From the **properties of plane shapes** students can develop the concept of **congruence**.

Applying proportional understanding to shapes leads to the concept of **similarity**.

Communicating mathematical reasoning begins with simple verbal explanations. It can then develop into formal methods of deductive **proof**.

The angle and chord properties in **circle geometry** provide opportunities to apply knowledge and skills, and uncover new relationships.

The study of geometry engages students in the intellectual stimulation of solving complex problems.

## Plane shapes

Each plane shape has a precise meaning in geometry and therefore a standard definition. Approximations of these plane shapes appear in the real world.

## Congruence

Plane shapes are congruent when they have the same shape and are the same size.

Congruent shapes can be superimposed on each other by rotation, translation or reflection, or a combination of these transformations.

## Similarity

If one plane figure can be enlarged so that it is congruent to the other plane figure, they are similar. One can be mapped to the other by a sequence of translations, rotations, reflections and enlargements.

## Geometric proof

Geometrical proof is a logical sequence of connected statements – with supporting reasons (previously established truths or theorems) – leading to an undeniable conclusion. This is called deductive proof.

## Circle geometry

Historically, the properties of the circle and its relationships were used extensively in geometric construction and design.