📐 Geometry & Trigonometry Refresher

What you’ll learn

1. Points, Lines and AnglesIdentify the basic objects of geometry and classify angles.Geometry is built from points, lines, rays and segments, and angles measure the turn between two rays in degrees. Angles are named acute, right, obtuse or straight by their size, read with a protractor.
2. TrianglesUse the triangle angle sum and classify triangles.Any triangle's interior angles total 180°, so two known angles give the third. Triangles are classified as equilateral, isosceles, scalene or right, and their rigidity makes them the basis of structural trusses.
3. The Pythagorean TheoremApply the Pythagorean theorem to right triangles.In a right triangle a² + b² = c², linking the two legs to the hypotenuse, so any two sides give the third. The 3-4-5 triangle is the classic example, and the theorem governs everyday right angles like a ladder on a wall.
4. Perimeter and AreaCompute perimeter and area of common shapes.Perimeter is the distance around a shape's boundary, while area is the space it encloses in square units, with formulas like l·w for a rectangle and ½·b·h for a triangle. Tiling a surface without gaps is area made visible.
5. CirclesUse π to find circumference and area of circles.Every circle shares the ratio π ≈ 3.14159, giving circumference = 2πr and area = πr². Circumference grows with the radius while area grows with its square, so doubling the radius quadruples the area.
6. Volume and Surface AreaCompute volume and surface area of solids.Volume measures the space a solid fills in cubic units (l·w·h for a box, πr²h for a cylinder), while surface area is its outer skin. A sphere minimises surface area for its volume, which is why bubbles are round and hexagons pack efficiently.
7. Similarity and CongruenceDistinguish congruence from similarity and use proportion.Congruent shapes match in size and shape; similar shapes share angles and proportional sides but differ in size. A known ratio between similar figures lets you compute unknown lengths, as in finding a tree's height from its shadow.
8. Introducing TrigonometryIntroduce sine, cosine and tangent via SOH-CAH-TOA.In a right triangle the side ratios depend only on the angle: sine = opp/hyp, cosine = adj/hyp, tangent = opp/adj. Because each ratio is fixed for a given angle, trig lets us compute inaccessible lengths like a pyramid's height from its shadow.
9. Solving with TrigonometrySolve right triangles and real problems with trig.Knowing one angle and one side, trig finds the rest by picking the ratio linking the known and unknown. Angles of elevation and depression, paired with a distance and the tangent ratio, let surveyors measure heights and depths they cannot reach.
10. The Unit Circle and WavesConnect the unit circle, radians and sine waves.On a unit circle a point at angle θ has coordinates (cos θ, sin θ), and its height traces the sine curve, extending trig beyond triangles. Radians measure angles by arc length, with 2π for a full circle, and the resulting sine wave describes ripples, sound and pendulums.

Questions this course answers

Grounded in trusted sources

• OpenStax — 'Geometry' and 'Algebra and Trigonometry' (openstax.org)
• OpenStax — 'Prealgebra'
• Khan Academy — Geometry and Trigonometry (khanacademy.org)
• Euclid, 'Elements' (public domain, T. L. Heath translation)

Every Wunder lesson is built from real, reputable sources — never invented.

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