Worked problem pages
Each page explains the idea, then works through real problems from the Mathyessy bank step by step.
Pythagorean theorem practice problemsFind missing sides of right triangles, spot Pythagorean triples and uncover the hidden right triangles that contest problems love.Special right triangles: 45-45-90 and 30-60-90 practiceTwo triangles show up in contest geometry again and again. Learn their side ratios once and you can skip the Pythagorean theorem.Triangle area practice problemsBase times height over two is only the start. Contest problems make you find the height, use a right triangle or reach for Heron's formula.Circle area and circumference practice problemsMost contest circle questions want an answer in terms of π. The real skill is finding the radius.Arc length and sector area practiceA sector is a slice of a circle. Work out what fraction of the circle you have, and the rest is the area or circumference formula.Polygon interior and exterior angle practiceFour short formulas cover almost every polygon angle question in middle school contests.Similar triangles and scale factor practiceSimilar figures have the same shape at different sizes. Know how lengths, areas and volumes scale and these problems become one-liners.Triangle inequality practice problemsCan three lengths make a triangle? One rule decides, and contest problems ask you to count how many lengths work.Prism and cube volume practiceEvery prism follows one rule: the area of the base times the height.Surface area practice problemsSurface area is the total area of every face. Picture unfolding the solid flat and add up the pieces.
Every Geometry practice set in Mathyessy
Each link opens that topic's question set in the free app. Questions get harder as you go, and you get instant feedback after each answer.
- Angle Basics
- Triangle Angle Sum
- Pythagorean Theorem · worked problems
- Special Right Triangles · worked problems
- Perimeter
- Rectangle Area
- Triangle Area · worked problems
- Parallelogram And Trapezoid
- Circumference
- Circle Area · worked problems
- Arcs And Sectors · worked problems
- Coordinate Distance
- Midpoint And Slope
- Similarity And Congruence · worked problems
- Transformations
- Prism Volume · worked problems
- Cylinder Volume
- Surface Area · worked problems
- Polygon Angles · worked problems
- Triangle Inequality · worked problems