Distinguish between conventions, definitions and derived properties.

Identify alternate angles and corresponding angles;

understand a proof that:

the sum of the angles of a triangle is 180° and of a quadrilateral is 360°;

the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Solve geometrical problems using side and angle properties of equilateral, isosceles and right-angled triangles and special quadrilaterals, explaining reasoning with diagrams and text; classify quadrilaterals by their geometric properties.

Use straight edge and compasses to construct:

the mid-point and perpendicular bisector of a line segment;

the bisector of an angle;

the perpendicular from a point to a line;

the perpendicular from a point on a line;

a triangle, given three sides (SSS);

use ICT to explore these constructions.

Understand congruence.

Core:

Distinguish between conventions, definitions and derived properties, practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, and the effect of varying them.

Explain how to find, calculate and use:

the sums of the interior and exterior angles of quadrilaterals, pentagons and hexagons,

the interior and exterior angles of regular polygons.

Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons, justifying inferences and explaining reasoning with diagrams and text.

Know the definition of a circle and the names of its parts; explain why inscribed regular polygons can be constructed by equal divisions of a circle.

Use straight edge and compasses to construct a triangle, given right angle, hypotenuse and side (RHS); use ICT to explore constructions of triangles and other 2-D shapes.

Apply the conditions SSS, SAS, ASA or RHS to establish the congruence of triangles.

Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio.

Find the locus of a point that moves according to a simple rule, both by reasoning and by using ICT.

Explore connections in mathematics across a range of contexts: shape and space.

Extension:

Understand and apply Pythagoras’ theorem.

Know that the tangent at any point on a circle is perpendicular to the radius at that point; explain why the perpendicular from the centre to the chord bisects the chord.

Know from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not.

Find the locus of a point that moves according to a more complex rule, involving loci and simple constructions.

## Objectives:

Support:Distinguish between conventions, definitions and derived properties.Identify alternate angles and corresponding angles;understand a proof that:the sum of the angles of a triangle is 180° and of a quadrilateral is 360°;Use straight edge and compasses to construct:the mid-point and perpendicular bisector of a line segment;the bisector of an angle;the perpendicular from a point to a line;the perpendicular from a point on a line;Understand congruence.Core:practical demonstration and proof; know underlying assumptions, recognising their importance and limitations, and the effect of varying them.Solve problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons,justifying inferences and explaining reasoning with diagrams and text.Apply the conditions SSS, SAS, ASA or RHS to establish the congruence of triangles.Know that if two 2-D shapes are similar, corresponding angles are equal and corresponding sides are in the same ratio.Extension:Understand and apply Pythagoras’ theorem.Know from experience of constructing them that triangles given SSS, SAS, ASA or RHS are unique, but that triangles given SSA or AAA are not.## Key Vocabulary:

), hypotenuse, right-angle, equilateral, isosceles, scalene, perpendicular bisector, loci, Pythagoras, hypotenuse, similar.## Suggested Lesson Outcomes:

SUPPORT TARGET

CORE## Framework:

## Teaching & Learning Resources:

Angle Rules Resources

Circles Resources

Triangle Resources

Proof Resources

Construction Resources

Loci Resources

Pythagoras Resources