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 • 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
- 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
- line and rotational symmetry of plane figures
- lines of symmetry
- order of rotational symmetry
- properties of triangles and 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 protractor where appropriate
- congruent and similar figures
- properties of similar triangles and quadrilaterals: • corresponding angles are equal • corresponding sides are proportional
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 reasonsG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Name the geometric condition before using an angle equality or sum.
- Line and rotational symmetryG1 Mathematics 2027 · Normal (Technical) Secondary 1 Mathematics 2020Test the whole figure under a reflection or rotation and count matching positions in a full turn.
- Triangle angle propertiesG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Use the angle sum and equal-side markings to justify unknown triangle angles.
- Parallel quadrilaterals and their anglesG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Use marked parallel sides and named quadrilateral properties to justify unknown angles.
- Triangle construction from dataG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Construct a triangle from stated lengths or angles and check that the data determine a possible figure.
- Bisectors and geometric constructionG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Use equal distances to justify compass constructions and check the given dimensions.
- Congruence and similarityG1 Mathematics 2027 · Normal (Technical) Secondary 2 Mathematics 2021Match corresponding parts before comparing lengths, angles and scale.
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