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Lessons by Ms Ho

Ms Ho specialises in plane geometry, circle theorems and triangle reasoning. Her lessons favour short written proofs with every construction justified.

34 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 segment7Angle between two planesSpatial Geometry · Ms Ho · cos φ = |n₁ · n₂| / (|n₁||n₂|)8Cube nets and surface areaSpatial Geometry · Ms Ho · surface area = 6a²9True height from an oblique sketchSpatial Geometry · Ms Ho · mark ⊥ before measuring height10Surface area of a square-based pyramidSpatial Geometry · Ms Ho · total SA = a² + 2aℓ11Converse of Pythagoras: proving a right anglePlane Geometry · Ms Ho · a² + b² = c² ⇒ angle opposite c is right12Heron’s formula when height is hiddenPlane Geometry · Ms Ho · s = (a+b+c)/213Exterior angle of a trianglePlane Geometry · Ms Ho · exterior = sum of remote interiors14Parallel lines and a transversalPlane Geometry · Ms Ho · alt = alt15Angle at the centre is twice the angle at the circumferencePlane Geometry · Ms Ho · ∠ at centre = 2 × ∠ at circumference16Cyclic quadrilateral: opposite anglesPlane Geometry · Ms Ho · ∠A + ∠C = 180°17AA similarity in two stepsPlane Geometry · Ms Ho · AA ⇒ similar18SAS congruence without mixing the anglePlane Geometry · Ms Ho · SAS, ASA, SSS, RHS19Tangent–secant length theoremPlane Geometry · Ms Ho · PT² = PA × PB20Midpoint theorem in a trianglePlane Geometry · Ms Ho · DE ∥ BC and DE = BC/221Basic proportionality (Thales) theoremPlane Geometry · Ms Ho · AD/DB = AE/EC22Angles in the same segmentPlane Geometry · Ms Ho · angles in the same segment are equal23Rhombus diagonals are perpendicular bisectorsPlane Geometry · Ms Ho · d₁² + d₂² = 4a²24Angle bisector theoremPlane Geometry · Ms Ho · BD/DC = AB/AC25Two tangents from an external pointPlane Geometry · Ms Ho · PT = QT26Rotation by 90° about the originCoordinates & Vectors · Ms Ho · 90° ACW: (x,y)→(−y,x)27Enlargement from a centreCoordinates & Vectors · Ms Ho · X′ = C + k(X − C)28Translation by a vectorCoordinates & Vectors · Ms Ho · (x,y) → (x+a,y+b)29Shortest path via a mirror lineCoordinates & Vectors · Ms Ho · reflect → straight line → intersect mirror30Ladder against a wallApplied & Exam · Ms Ho · ladder² = height² + base²31Exact trig values you should not calculatorApplied & Exam · Ms Ho · sin30=1/232Compound shapes: add and subtract areasApplied & Exam · Ms Ho · A = A₁ + A₂ − overlap33Calculator degree mode and inverse trigApplied & Exam · Ms Ho · θ = tan⁻¹(opp/adj) in DEG mode34Arc length and sector areaPlane Geometry · Ms Ho · arc = 2πr·(θ/360°)