5 Course 5 of 10
Geometry
High school geometry from the ground up: start with points, lines and angles, prove triangles congruent, explore circles and area, and finish with right triangles and similarity. Every lesson has examples worked step by step, practice problems with solutions and a quick check at the end.
Before you start: Solving linear equations and working with square roots.
Unit 1 Foundations
- 1 Points, lines, planes and segments The undefined terms of geometry, the first postulates, rays and segments, the segment addition postulate and the midpoint of a segment. 10 min
- 2 Angles and angle pairs Measuring and classifying angles, the angle addition postulate, complementary and supplementary angles, linear pairs, vertical angles and angle bisectors. 11 min
Unit 2 Triangles
- 3 Triangles and their angles Classifying triangles, the triangle sum theorem, the exterior angle theorem, the triangle inequality and the base angles of isosceles triangles. 12 min
- 4 Triangle congruence Congruent triangles and corresponding parts, the SSS, SAS, ASA, AAS and HL congruence shortcuts, why SSA and AAA don't work, and CPCTC in proofs. 13 min
- 5 Bisectors, medians, altitudes and triangle centers Perpendicular bisectors, angle bisectors, medians and altitudes of a triangle, and the four points of concurrency: circumcenter, incenter, centroid and orthocenter. 12 min
Unit 3 Parallel lines and quadrilaterals
- 6 Parallel lines, transversals and polygon angles The angle pairs formed by a transversal, what happens when the lines are parallel, how to prove lines parallel, and the angle sums of polygons. 12 min
- 7 Quadrilaterals Properties of parallelograms, rectangles, rhombuses, squares, trapezoids and kites, including diagonals and the trapezoid midsegment, with algebra problems. 13 min
Unit 4 Circles
- 8 Circles, arcs, chords and tangents The parts of a circle, central angles and arc measures, the inscribed angle theorem, tangent lines and chords. 13 min
- 9 Inscribed and circumscribed polygons When a polygon can be inscribed in a circle or circumscribed about one, cyclic and tangential quadrilaterals, and the center, radius and apothem of regular polygons. 11 min
Unit 5 Area
- 10 Area of polygons Area formulas for rectangles, parallelograms, triangles, trapezoids, rhombuses, kites and regular polygons, where they come from, and how area changes with scale. 13 min
- 11 Circumference and area of circles The number pi, circumference and area of a circle, arc length, area of a sector, and the area of shaded regions. 11 min
Unit 6 Right triangles and similarity
- 12 The Pythagorean theorem and special right triangles The Pythagorean theorem and its converse, classifying triangles as acute, right or obtuse, Pythagorean triples, and 45-45-90 and 30-60-90 triangles. 14 min
- 13 Similarity in right triangles and the geometric mean How the altitude to the hypotenuse splits a right triangle into similar triangles, the geometric mean, and the altitude and leg rules for solving right triangles. 12 min
- 14 Similar triangles Similar figures and scale factors, the AA, SSS and SAS similarity criteria, the triangle proportionality theorem, perimeter and area ratios, and indirect measurement. 13 min