Geometry and reasoning
Build and connect the representations and methods in geometry and reasoning.
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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 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
- 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, 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
- solving simple problems involving congruence and similarity
- 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
- 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
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About lesson progress
Lesson marks record what you have studied. Checks show understanding separately. Guest marks come from this device.
- Parallel lines and angle reasonsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Name the geometric condition before using an angle equality or sum.
- Line and rotational symmetryG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Test the whole figure under a reflection or rotation and count matching positions in a full turn.
- Triangle angle propertiesG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use the angle sum and equal-side markings to justify unknown triangle angles.
- Parallel quadrilaterals and their anglesG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Use marked parallel sides and named quadrilateral properties to justify unknown angles.
- Polygon angle sumsG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Distinguish totals for a convex polygon from equal individual angles in a regular polygon.
- Triangle construction from dataG3 Mathematics 2027 · Express Secondary 1 Mathematics 2020Construct a triangle from stated lengths or angles and check that the data determine a possible figure.
- Bisectors and geometric constructionG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Use equal distances to justify compass constructions and check the given dimensions.
- Congruence and similarityG3 Mathematics 2027 · Express Secondary 2 Mathematics 2021Match corresponding parts before comparing lengths, angles and scale.
- Triangle tests and similar-solid scalesG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Use sufficient corresponding data and distinguish length, area and volume scale factors.
- Circle angle and tangent propertiesG3 Mathematics 2027 · Express Secondary 3–4 Mathematics 2022Identify the chord, arc, radius and tangent that justify each circle relationship.
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