Angles, polygons, symmetry, similar figures and circle properties topic check · G3 Mathematics

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Geometry and reasoning

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Geometry and reasoning

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Geometry and reasoning

Parallel-line relationships and angle values · Check your progress

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Geometry and reasoning

Similar-triangle scale factors and lengths · Check your progress

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Geometry and reasoning

Length, area and volume scales of similar figures · Check your progress

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Geometry and reasoning

Angle types, angles on a line, at a point and vertically opposite · Check your progress

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Geometry and reasoning

Angles in combined triangles · Check your progress

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Geometry and reasoning

Angles in parallelograms and trapeziums · Check your progress

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Geometry and reasoning

Lines of symmetry and order of rotational symmetry · Check your progress

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Geometry and reasoning

Perpendicular bisector and angle bisector properties · Check your progress

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Geometry and reasoning

Interior and exterior angles of polygons · Check your progress

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Geometry and reasoning

Classify special quadrilaterals · Check your progress

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Geometry and reasoning

Angles from circle properties · Check your progress

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Geometry and reasoning

Lengths from circle symmetry properties · Check your progress

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Geometry and reasoning

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Geometry and reasoning

Parallel-line relationships and angle values · Check again

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Geometry and reasoning

Similar-triangle scale factors and lengths · Check again

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Geometry and reasoning

Length, area and volume scales of similar figures · Check again

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Geometry and reasoning

Angle types, angles on a line, at a point and vertically opposite · Check again

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Geometry and reasoning

Angles in combined triangles · Check again

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Geometry and reasoning

Angles in parallelograms and trapeziums · Check again

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Geometry and reasoning

Lines of symmetry and order of rotational symmetry · Check again

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Geometry and reasoning

Perpendicular bisector and angle bisector properties · Check again

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Geometry and reasoning

Interior and exterior angles of polygons · Check again

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Geometry and reasoning

Classify special quadrilaterals · Check again

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Geometry and reasoning

Angles from circle properties · Check again

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Geometry and reasoning

Lengths from circle symmetry properties · Check again

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Geometry and reasoning

Retention check

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Geometry and reasoning

Parallel-line relationships and angle values · Retention check

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Geometry and reasoning

Similar-triangle scale factors and lengths · Retention check

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Geometry and reasoning

Length, area and volume scales of similar figures · Retention check

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Geometry and reasoning

Angle types, angles on a line, at a point and vertically opposite · Retention check

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Geometry and reasoning

Angles in combined triangles · Retention check

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Geometry and reasoning

Angles in parallelograms and trapeziums · Retention check

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Geometry and reasoning

Lines of symmetry and order of rotational symmetry · Retention check

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Geometry and reasoning

Perpendicular bisector and angle bisector properties · Retention check

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Geometry and reasoning

Interior and exterior angles of polygons · Retention check

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Geometry and reasoning

Classify special quadrilaterals · Retention check

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Geometry and reasoning

Angles from circle properties · Retention check

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Geometry and reasoning

Lengths from circle symmetry properties · Retention check

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Geometry and reasoning

Practise: Parallel-line relationships and angle values

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Geometry and reasoning

Practise: Similar-triangle scale factors and lengths

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Geometry and reasoning

Practise: Length, area and volume scales of similar figures

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Geometry and reasoning

Practise: Angle types, angles on a line, at a point and vertically opposite

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Geometry and reasoning

Practise: Angles in combined triangles

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Geometry and reasoning

Practise: Angles in parallelograms and trapeziums

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Geometry and reasoning

Practise: Lines of symmetry and order of rotational symmetry

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Geometry and reasoning

Practise: Perpendicular bisector and angle bisector properties

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Geometry and reasoning

Practise: Interior and exterior angles of polygons

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Geometry and reasoning

Practise: Classify special quadrilaterals

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Geometry and reasoning

Practise: Angles from circle properties

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Geometry and reasoning

Practise: Lengths from circle symmetry properties

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Geometry and reasoning

Revision notes

Revise geometry and reasoning

Build geometric arguments from angle, circle and similarity properties, and distinguish length, area and volume scale factors.

Key ideas

Parallel lines and angle reasons
Name the geometric condition before using an angle equality or sum.
Angle relations and equations
Trace every angle pair, choose equality or a sum, and check algebraic results against the geometry.
Line and rotational symmetry
Test the whole figure under a reflection or rotation and count matching positions in a full turn.
Triangle angle properties
Use the angle sum and equal-side markings to justify unknown triangle angles.
Parallel quadrilaterals and their angles
Use marked parallel sides and named quadrilateral properties to justify unknown angles.
Polygon angle sums
Distinguish totals for a convex polygon from equal individual angles in a regular polygon.
Triangle construction from data
Construct a triangle from stated lengths or angles and check that the data determine a possible figure.
Bisectors and geometric construction
Use equal distances to justify compass constructions and check the given dimensions.
Congruence and similarity
Match corresponding parts before comparing lengths, angles and scale.
Similar triangles and unknown lengths
Match corresponding vertices, find the scale factor and calculate unknown sides in separate, nested and crossed triangles.
Enlargement, reduction and scale drawings
Use one scale factor for every length, keep angles unchanged, and move between real lengths and a scale drawing.
Triangle tests and similar-solid scales
Use sufficient corresponding data and distinguish length, area and volume scale factors.
Circle angle and tangent properties
Identify the chord, arc, radius and tangent that justify each circle relationship.

What the syllabus asks

From the G3 Mathematics 2027 syllabus

Show all 18 syllabus statements

Right, acute, obtuse and reflex angles
Vertically opposite angles, angles on a straight line and angles at a point
Angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
Properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties
Classifying special quadrilaterals on the basis of their properties
Angle sum of interior and exterior angles of any convex polygon
Construction of simple geometrical figures from given data using compasses, ruler, set squares and protractors, where appropriate
Congruent figures and similar figures
Properties of similar triangles and polygons: - corresponding angles are equal - corresponding sides are proportional
Enlargement and reduction of a plane figure
Scale drawings
Properties and construction of perpendicular bisectors of line segments and angle bisectors
Determining whether two triangles are - congruent - similar
Ratio of areas of similar plane figures
Ratio of volumes of similar solids
Solving simple problems involving similarity and congruence
Symmetry properties of circles: - equal chords are equidistant from the centre - the perpendicular bisector of a chord passes through the centre - tangents from an external point are equal in length - the line joining an external point to the centre of the circle bisects the angle between the tangents
Angle properties of circles: - angle in a semicircle is a right angle - angle between tangent and radius of a circle is a right angle - angle at the centre is twice the angle at the circumference - angles in the same segment are equal - angles in opposite segments are supplementary

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Revise geometry and reasoning

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What the syllabus asks