14:26
Geometry
Intro
Points, Lines & Planes
The three things geometry refuses to define, and why that is deliberate.
Geometry
Geometry is the course where you stop taking results on trust and start proving them. It is also the one that looks least like the algebra either side of it, which catches students out. The reasoning skills built here — stating what you know, justifying every step, spotting what a diagram does and does not tell you — are what the rest of mathematics assumes you have.
43 topics · 7 units
43
Topics
Proof, congruence, similarity and the shapes algebra describes.
Foundations & Proof
6 topicsThe undefined terms everything is built from, and the reason geometry is the course where you finally have to prove things.
14:26
15:14
Geometry
Intro
Segment Addition & Midpoints
Adding lengths along a line, and finding the exact middle.
14:24
Geometry
Intro
Angle Relationships
Vertical, linear, complementary and supplementary pairs, used as equations.
7:07
Geometry
Core
Parallel Lines & Transversals
Eight angles, two sizes, and the converses that prove lines parallel.
11:54
Geometry
Core
Conditional Statements & Logic
If-then statements, their converse, inverse and contrapositive.
11:40
Geometry
Advanced
Writing Two-Column Proofs
Statements on the left, reasons on the right, and how to get unstuck.
Triangles & Congruence
9 topicsThe centre of the course. Five congruence criteria, what they unlock, and the special segments inside every triangle.
12:40
3:56
Geometry
Core
What Congruence Means
Same shape and size, defined by motion rather than by measurement.
29:22
15:24
Geometry
Core
Proving Congruence: ASA, AAS & HL
The angle-based criteria, and the one reserved for right triangles.
3:53
9:03
Geometry
Core
Isosceles & Equilateral Triangles
Equal sides force equal angles, and the converse holds too.
5:52
Geometry
Core
Triangle Inequalities
Which three lengths can actually form a triangle, and which angle is biggest.
17:56
Geometry
Advanced
Medians, Altitudes & Centres
Four segments, four points of concurrency, and what each one does.
3:07
Geometry
Core
The Midsegment Theorem
Join two midpoints and you get a parallel segment, half as long.
Similarity & Right Triangles
7 topicsSame shape at a different scale, and the right-triangle results that fall out of it.
4:54
Geometry
Core
Similar Polygons
Equal angles, proportional sides, and what scaling does to perimeter and area.
29:22
Geometry
Core
Triangle Similarity: AA, SSS & SAS
Why two angles are enough to prove triangles similar.
23:53
Geometry
Advanced
The Side-Splitter Theorem
A line parallel to one side cuts the other two proportionally.
24:50
Geometry
Advanced
Geometric Mean in Right Triangles
Drop an altitude to the hypotenuse and three similar triangles appear.
2:48
Geometry
Core
Practice ready
The Converse & Pythagorean Triples
Using a² + b² = c² backwards to classify any triangle.
11:11
Geometry
Core
Practice ready
Special Right Triangles
45-45-90 and 30-60-90, and the shortcuts they give you.
10:33
Quadrilaterals & Polygons
5 topicsThe family tree of four-sided figures, what each one guarantees, and how to prove which is which.
9:10
Geometry
Intro
Polygon Angle Sums
Interior angles grow with the number of sides; exterior angles never do.
20:51
11:02
Geometry
Core
Rectangles, Rhombuses & Squares
Three special parallelograms and the diagonal test for each.
13:36
11:08
Geometry
Advanced
Practice ready
Proving Quadrilateral Types
Choosing the least work needed to classify a shape.
Circles
7 topicsAngles, arcs, chords and tangents — a set of theorems that all reduce to one relationship.
32:30
Geometry
Intro
Circle Vocabulary
Radius, chord, secant, tangent, and the words the theorems depend on.
32:30
14:16
32:30
Geometry
Advanced
Angles from Tangents & Secants
Vertex inside gives half the sum; vertex outside gives half the difference.
32:30
Geometry
Advanced
Chords, Arcs & Segment Lengths
Perpendicular bisectors through the centre, and the products that stay equal.
15:57
3:51
Area, Volume & Solids
5 topicsMeasuring flat figures precisely, then moving into three dimensions.
23:34
13:55
3:17
5:29
Geometry
Advanced
Cross-Sections & Solids of Revolution
Slicing a solid, and spinning a flat shape into one.
5:22
Coordinate Geometry & Transformations
4 topicsWhere geometry and algebra meet: proving theorems with formulas, and defining congruence by motion.
9:39
Geometry
Intro
Practice ready
Distance & Midpoint Formulas
The Pythagorean theorem and an average, doing most of coordinate geometry.
9:06
Geometry
Advanced
Coordinate Proofs
Proving a theorem for every case by using variables instead of numbers.
7:22
Geometry
Core
Rigid Motions & Symmetry
Translations, reflections, rotations, and the symmetry they reveal.
4:59
Geometry
Core
Dilations & Similarity Transformations
The one transformation that changes size, and what it preserves.