Back to Geometry and reasoning

Angles, shape properties, symmetry and similar triangles topic check

Practise angles, shape properties, symmetry and similar triangles in G1 Mathematics, check independently, and return later to review. This check covers selected skills, not the whole course topic.

Learning goals

Classify angles by their size
Apply the sum of angles around a point
Deduce all unknown angles at two intersecting lines
Connect triangle, rectangle and square facts to deduce angles in a drawn composite figure
Connect parallelogram and connected shape facts to deduce angles using existing lines
Connect trapezium and connected shape facts to deduce angles using existing lines
Use the equal-distance properties of perpendicular bisectors and angle bisectors
Produce complete parallel-line angle relations and values from numerical or affine-expression givens
Construct geometric figures from stated conditions
Give the number of lines of symmetry and the order of rotational symmetry of a plane figure
Find a scale factor and unknown lengths from matched sides of similar triangles
Reason about congruence, similarity and scale factors

G1 Mathematics 2027

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Choose a practice setParallel-line relationships and angle values · 3 questionsSimilar-triangle scale factors and lengths · 4 questionsAngle types, angles on a line, at a point and vertically opposite · 6 questionsAngles in combined triangles · 2 questionsAngles in parallelograms and trapeziums · 4 questionsLines of symmetry and order of rotational symmetry · 2 questionsPerpendicular bisector and angle bisector properties · 2 questionsAll skills in this check

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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

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

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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 again

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Geometry and reasoning

Similar-triangle scale factors and lengths · 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

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

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

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: 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

Revision notes

Revise geometry and reasoning

Use angle and symmetry properties, construct triangles and bisectors, and match corresponding parts in congruent or similar figures.

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.
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.

What the syllabus asks

From the G1 Mathematics 2027 syllabus

Show all 11 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
Properties of perpendicular bisectors of line segments and angle bisectors
Construction of simple geometrical figures from given data (including perpendicular bisectors and angle bisectors) using compasses, ruler, set squares and protractors, where appropriate
Line and rotational symmetry of plane figures
Lines of symmetry
Order of rotational symmetry
Congruent and similar figures
Properties of similar triangles and quadrilaterals: ∗ corresponding angles are equal ∗ corresponding sides are proportional