This grade 8 pythagorean theorem test checks the pythagorean theorem in 45 minutes, with 9 questions for a total of 20 points.
This 45-minute test covers Common Core standards 8.G.B.6 and 8.G.B.7. It has 9 questions worth 20 points in total. Show your work and include units. Calculators are allowed for square roots, but write the equation before using one.
- Grade: Grade 8
- Chapter: The Pythagorean Theorem
- Common Core: 8.G.B.6, 8.G.B.7
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 2 pts; Question 4: 3 pts; Question 5: 2 pts; Question 6: 2 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 2 pts)
Grade 8 Pythagorean Theorem Test: questions 1–5
Question 1: Hypotenuse (2 points)
Find the length of the hypotenuse.
Question 2: Missing leg (2 points)
A right triangle has a hypotenuse of 26 ft and one leg of 10 ft. Find the length of the other leg.
Question 3: Rounded hypotenuse (2 points)
The legs of a right triangle are 5 in. and 9 in. Find the hypotenuse to the nearest tenth of an inch.
Question 4: Right triangle or not (3 points)
For each set of side lengths, decide whether the triangle is a right triangle. Show your calculation.
- 12 in., 35 in., 37 in. (1 point)
- 10 in., 24 in., 27 in. (1 point)
- 16 in., 30 in., 34 in. (1 point)
Question 5: Area proof (2 points)
A square with side length 7 in. is divided into four congruent right triangles with legs 3 in. and 4 in. and a tilted square in the middle.
- Find the area of the tilted square. (1 point)
- Find the side length of the tilted square. (1 point)
Grade 8 Pythagorean Theorem Test: questions 6–9
Question 6: Ladder (2 points)
A 17-ft ladder reaches a window that is 15 ft above the ground. How far is the base of the ladder from the wall?
Question 7: TV screen (3 points)
The diagonal of a TV screen measures 50 in. and the screen is 40 in. wide.
- Find the height of the screen. (2 points)
- Find the area of the screen. (1 point)
Question 8: Rod in a box (2 points)
A box is 24 in. long, 10 in. wide and 6 in. tall. Can a straight 30-in. rod fit inside the box? Justify your answer.
Question 9: Cutting across the park (2 points)
A park is a rectangle 120 yd long and 50 yd wide. Aisha runs from one corner to the opposite corner along the diagonal path instead of along two sides. How many yards shorter is the diagonal route?
How to use this grade 8 pythagorean theorem test
Take this grade 8 pythagorean theorem test without notes, then grade it with the test answer key out of 20 points.
See every chapter on the Grade 8 math page.