This course moves geometry from measuring to proving. You start by proving the familiar angle facts about intersecting lines, parallel lines and triangles. Then you learn the congruence rules SAS, ASA, AAS, SSS and RHS and use them to prove properties of isosceles triangles, parallelograms, rectangles and rhombuses, together with the triangle inequality and the mid-point theorem. Next come similar triangles: the basic proportionality theorem, the similarity tests, areas of similar triangles and a proof of Pythagoras' theorem. The course ends with circles: chords, angles at the centre and on the circle, cyclic quadrilaterals and tangents.
Middle Years
Plane Geometry (Level 2)
Geometry with proofs: angles and parallel lines, congruent triangles, isosceles triangles and inequalities, parallelograms, the mid-point theorem, similar triangles, Pythagoras' theorem, and chords, angles and tangents of circles.
- 9 lessons
Overview
Lessons
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Angles and parallel lines, with proofs
Linear pairs, vertically opposite angles, angles made by a transversal with parallel lines, and proofs of the angle sum and exterior angle properties of a triangle.
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Congruence of triangles
What congruent triangles are, why the order of letters matters, the rules SAS, ASA, AAS, SSS and RHS, CPCT, and how to write a congruence proof.
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Isosceles triangles and inequalities
Equal sides face equal angles, a longer side faces a larger angle, and any two sides of a triangle add up to more than the third.
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Quadrilaterals and parallelograms
The angle sum of a quadrilateral, the properties of a parallelogram and how to recognise one, and the diagonals of rectangles, rhombuses and squares.
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The mid-point theorem
The segment joining the midpoints of two sides of a triangle is parallel to the third side and half of it: proof, converse, trapeziums and quadrilaterals.
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Similar triangles
What similar means, the basic proportionality theorem and its converse, the AA, SSS and SAS tests, and heights found from shadows.
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Areas of similar triangles and Pythagoras' theorem
Areas of similar triangles are in the ratio of the squares of their sides; a proof of Pythagoras' theorem and its converse, with triples and applications.
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Circles: chords and angles
Equal chords, the perpendicular from the centre, the angle at the centre being double the angle on the circle, angles in a semicircle and cyclic quadrilaterals.
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Tangents to a circle
A tangent is perpendicular to the radius, tangents from an outside point are equal, the angle between two tangents, and figures drawn around a circle.