8th Grade The Pythagorean Theorem Worksheet (PDF)
This pythagorean theorem worksheet for 8th Grade covers the pythagorean theorem (Common Core 8.G.B.6, 8.G.B.7), with a free PDF to print.
These 20 problems practice the Pythagorean theorem, its converse and applications in two and three dimensions (Common Core 8.G.B.6 and 8.G.B.7). Each problem has its own space for work, so print the page and write directly on it.
The problems start with direct skill checks and grow harder as you go. Later items use the converse, three dimensions and real situations such as ladders and ramps. Use the answer key afterwards to check every step.
Grade 8 · Common Core State Standards: 8.G.B.6, 8.G.B.7
Pythagorean theorem worksheet: exercises 1 to 10
Exercise 1 – Find the hypotenuse
Find the hypotenuse of a right triangle with legs 6 inches and 8 inches.
Exercise 2 – Another triple
Exercise 3 – Find a leg
Exercise 4 – Not a whole number
Exercise 5 – Is it a right triangle?
Exercise 6 – Not a right triangle
Exercise 7 – Ladder
A 13-foot ladder leans on a wall with its base 5 feet from the wall. How high up the wall does it reach?
Exercise 8 – Rectangle diagonal
A rectangular patio is 12 feet by 9 feet. How long is its diagonal?
Exercise 9 – TV screen
Exercise 10 – Isosceles right triangle
Exercises 11 and up
Exercise 11 – Perimeter
Exercise 12 – Test the converse
Exercise 13 – 3D box
Find the length of the space diagonal of a box with edges 3, 4 and 12.
Exercise 14 – Smaller box
Exercise 15 – Baseball diamond
The bases on a Little League field are 90 feet apart. How far is a throw from home plate to second base? Round to the nearest tenth.
Exercise 16 – Ramp
A ramp rises 5 feet over a horizontal distance of 12 feet. How long is the ramp?
Exercise 17 – Kite string
Exercise 18 – Shortcut
Exercise 19 – Phone screen
Exercise 20 – Explain
Key facts behind this pythagorean theorem worksheet
- \(a^{2} + b^{2} = c^{2}\), where \(c\) is the hypotenuse.
- To find a leg: \(a^{2} = c^{2} – b^{2}\).
- Converse: if \(a^{2} + b^{2} = c^{2}\), the triangle has a right angle.
- Common triples: 3-4-5, 5-12-13, 8-15-17 and their multiples.
- The theorem works in 3D: the space diagonal satisfies \(d^{2} = a^{2} + b^{2} + c^{2}\).
How to use this pythagorean theorem worksheet
Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.
Download the pythagorean theorem worksheet as a PDF with the button below and keep it with your notes.
All Grade 8 chapters: Grade 8 math.
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