Geometry and reasoning
Build and connect the representations and methods in geometry and reasoning.
More
Offline pages
Saved on this device only. Connect at least once every 30 days to confirm Premium. Sign-out or a change of account removes saved copies.
Find this activity in your course
Before you begin
Build and connect the representations and methods in geometry and reasoning.
Learning goals
- Deduce unknown angles from geometric relationships
- Classify angles by their size
- Classify shapes by their properties
- Construct geometric figures from stated conditions
- Reason about congruence, similarity and scale factors
Syllabus statements covered
- 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 protractor, where appropriate
- congruent 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 • 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 All circle properties in this row are tested only in Paper 2 Section B.
- right, acute, obtuse and reflex angles
- vertically opposite angles, angles on a straight line, angles at a point
- angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles
- properties of triangles
- properties of 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
- 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
- solving simple problems involving congruence and similarity
- 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
Lessons
Work through them in order.
About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Parallel lines and angle reasonsG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020Name the geometric condition before using an angle equality or sum.
- Line and rotational symmetryG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Test the whole figure under a reflection or rotation and count matching positions in a full turn.
- Triangle angle propertiesG2 Mathematics 2027 · Normal (Academic) Secondary 1 Mathematics 2020Use the angle sum and equal-side markings to justify unknown triangle angles.
- Parallel quadrilaterals and their anglesG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Use marked parallel sides and named quadrilateral properties to justify unknown angles.
- Polygon angle sumsG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Distinguish totals for a convex polygon from equal individual angles in a regular polygon.
- Triangle construction from dataG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Construct a triangle from stated lengths or angles and check that the data determine a possible figure.
- Bisectors and geometric constructionG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Use equal distances to justify compass constructions and check the given dimensions.
- Congruence and similarityG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021 · Normal (Academic) Secondary 3–4 Mathematics 2022Match corresponding parts before comparing lengths, angles and scale.
- Circle angle and tangent propertiesG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Identify the chord, arc, radius and tangent that justify each circle relationship.
No lessons match your search. Try a shorter phrase, or show all lessons.