Grade 8 Pythagorean Theorem Test PDF Sample
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Answer key included
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Assessment balance
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PDF preview
1. A right triangle has legs of 8 cm and 15 cm. Find the hypotenuse.
2. A 25-foot ladder reaches 24 feet up a wall. How far is its base from the wall?
3. Find the distance between (1, 2) and (7, 10).
Preview shows representative problems from the printable student-facing PDF.
Answer key preview
1. 17 cm
c² = 8² + 15² = 64 + 225 = 289, so c = √289 = 17.
2. 7 feet
The ladder is the hypotenuse: b² = 25² − 24² = 625 − 576 = 49, so b = 7.
3. 10
Horizontal change 6, vertical change 8: √(6² + 8²) = √100 = 10.
Worked answers help teachers verify explanation depth, not just final-answer accuracy.
Skills assessed
- Finding a missing hypotenuse or leg (8.G.7)
- Using the converse to identify right triangles (8.G.6)
- Distance between two points on the coordinate plane (8.G.8)
- Real-world right-triangle applications
Difficulty balance
5 easy hypotenuse and missing-leg items, 3 medium converse and coordinate-distance problems, 2 hard multi-step real-world applications
Teacher use case
Useful as a unit test after the Pythagorean theorem, a review before high school geometry, or a make-up paper with the same difficulty profile.
Common student mistakes to watch for
- Adding the squares when finding a leg instead of subtracting from the hypotenuse squared
- Forgetting to take the square root at the end
- Calling a triangle right-angled without checking that a² + b² = c²
FAQ
Can I print this Grade 8 Pythagorean Theorem sample?
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Yes. Each sample page includes an answer key preview with worked reasoning so teachers can evaluate grading clarity.
Can I generate a harder or easier version?
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