ShieldsGeometry
Spatial GeometryPlane GeometryCoordinates & VectorsApplied & ExamExam papers
Home / Lessons / Plane Geometry

Plane Geometry

Triangles, similarity, circle theorems and short written proofs.

26 lessons

1Circle tangents: the radius is perpendicularPlane Geometry · Ms Ho · tangent ⟂ radius at the point of contact2Right-triangle lengths: Pythagoras and altitudePlane Geometry · Ms Ho · a² = b² + c²3Similar triangles: matching sides in proportionPlane Geometry · Ms Ho · AB/DE = BC/EF = AC/DF4Chord theorem: perpendicular from the centrePlane Geometry · Ms Ho · OM ⟂ AB ⇒ AM = MB5Isosceles triangles and equal base anglesPlane Geometry · Ms Ho · AB = AC ⇒ ∠ABC = ∠ACB6Alternate segment theorem with a short proofPlane Geometry · Ms Ho · ∠ between tangent and chord = angle in alternate segment7Converse of Pythagoras: proving a right anglePlane Geometry · Ms Ho · a² + b² = c² ⇒ angle opposite c is right8Heron’s formula when height is hiddenPlane Geometry · Ms Ho · s = (a+b+c)/29Exterior angle of a trianglePlane Geometry · Ms Ho · exterior = sum of remote interiors10Parallel lines and a transversalPlane Geometry · Ms Ho · alt = alt11Angle at the centre is twice the angle at the circumferencePlane Geometry · Ms Ho · ∠ at centre = 2 × ∠ at circumference12Cyclic quadrilateral: opposite anglesPlane Geometry · Ms Ho · ∠A + ∠C = 180°13AA similarity in two stepsPlane Geometry · Ms Ho · AA ⇒ similar14SAS congruence without mixing the anglePlane Geometry · Ms Ho · SAS, ASA, SSS, RHS15Tangent–secant length theoremPlane Geometry · Ms Ho · PT² = PA × PB16Height and area of an equilateral trianglePlane Geometry · Ms Tam · h = (√3/2)a17Midpoint theorem in a trianglePlane Geometry · Ms Ho · DE ∥ BC and DE = BC/218Basic proportionality (Thales) theoremPlane Geometry · Ms Ho · AD/DB = AE/EC19Angles in the same segmentPlane Geometry · Ms Ho · angles in the same segment are equal20Rhombus diagonals are perpendicular bisectorsPlane Geometry · Ms Ho · d₁² + d₂² = 4a²21Area of a trapeziumPlane Geometry · Ms Tam · area = ½(a+b)h22Sine rule for a non-right trianglePlane Geometry · Mr Wong · a/sin A = b/sin B = c/sin C23Cosine rule to find a sidePlane Geometry · Mr Wong · c² = a² + b² − 2ab cos C24Angle bisector theoremPlane Geometry · Ms Ho · BD/DC = AB/AC25Two tangents from an external pointPlane Geometry · Ms Ho · PT = QT26Arc length and sector areaPlane Geometry · Ms Ho · arc = 2πr·(θ/360°)