## Core concept 6.1

## Geometrical properties

6.1.1.1* Understand that a pair of parallel lines traversed by a straight line produces sets of equal and supplementary angles

6.1.1.2* Know and understand proofs that in a triangle, the sum of interior angles is 180 degrees

6.1.1.3 Know and understand proofs for finding the interior and exterior angle of any regular polygon

6.1.1.4 Solve problems that require use of a combination of angle facts to identify values of missing angles, providing explanations of reasoning and logic used

### 6.1.1.1 Understand that a pair of parallel lines traversed by a straight line produces sets of equal and supplementary angles

●Recognise that two intersecting lines create two pairs of equal and opposite angles.

●Recognise that adding another line parallel to the original creates a further two pairs of equal and opposite angles that are identical to the original four.

●Identify angles in more complex diagrams.

Desmos Activities on Parallel Lines

6.1.2.1 Recognise that similar shapes have sides in proportion to each other but angle sizes are preserved

6.1.2.2 Recognise that for congruent shapes both side lengths and angle sizes are preserved

6.1.2.3 Understand and use the criteria by which triangles are congruent

6.1.2.4 Recognise rotational symmetry in shapes

6.1.3.1 Be aware that there is a relationship between the lengths of the sides of a right-angled triangle

6.1.3.2* Use and apply Pythagoras' theorem to solve problems in a range of contexts

### 6.1.3.2 Use and apply Pythagoras’ theorem to solve problems in a range of contexts

●Identify when Pythagoras’ theorem can be applied.

●Solve problems using Pythagoras’ theorem to calculate lengths.

●Solve problems using Pythagoras’ theorem to make statements about angles.