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Pythagorean Theorem | Grade 8

Student Concept Worksheet Answers
1
c = 15
9² + 12² = 81 + 144 = 225 = c². So c = 15. (This is the 3-4-5 triple times 3)
2
a = 15
a² + 8² = 17². a² + 64 = 289. a² = 225. a = 15. (This is the 8-15-17 triple)
3
Distance = 5
Horizontal: 6-2=4. Vertical: 4-1=3. Distance: 4² + 3² = 16 + 9 = 25. c = 5. (3-4-5 triple)
4
Ladder = 10 feet
6² + 8² = c². 36 + 64 = 100. c = 10. (This is the 3-4-5 triple times 2)
Practice Worksheet Answers

Part A: Finding the Hypotenuse

#AnswerWork
1c = 53² + 4² = 9 + 16 = 25, c = 5
2c = 135² + 12² = 25 + 144 = 169, c = 13
3c = 178² + 15² = 64 + 225 = 289, c = 17
4c = 419² + 40² = 81 + 1600 = 1681, c = 41

Part B: Finding a Missing Leg

#AnswerWork
5a = 8a² + 36 = 100, a² = 64, a = 8
6a = 12a² + 81 = 225, a² = 144, a = 12
7a = 2449 + a² = 625, a² = 576, a = 24
8a = 21400 + a² = 841, a² = 441, a = 21

Part C: Distance Between Points

9
Distance = 5 units
Horizontal: 4-1=3, Vertical: 5-1=4. 3² + 4² = 25, c = 5
10
Distance = 10 units
Horizontal: 10-2=8, Vertical: 9-3=6. 8² + 6² = 64 + 36 = 100, c = 10
11
Distance = 5 units
Horizontal: 1-(-2)=3, Vertical: 5-1=4. 3² + 4² = 25, c = 5

Part D: Word Problems

12
Diagonal = 40 inches
32² + 24² = 1024 + 576 = 1600, c = 40
13
Ladder = 13 feet
5² + 12² = 25 + 144 = 169, c = 13 (5-12-13 triple)
14
Distance = 127.3 feet
90² + 90² = 8100 + 8100 = 16200, c = 127.28... (approx 127.3)
15
Distance = 17 miles
8² + 15² = 64 + 225 = 289, c = 17 (8-15-17 triple)

Challenge Questions:

#16: First find diagonal of base: 3² + 4² = 25, so base diagonal = 5. Then use that with height: 5² + 12² = 25 + 144 = 169, space diagonal = 13 inches.

#17: No, it's NOT a right triangle. Check: 7² + 11² = 49 + 121 = 170. But 13² = 169. Since 170 ≠ 169, this is not a right triangle. (The triangle is slightly obtuse.)

FAST Practice Quiz Answers
1
A) 10 inches
6² + 8² = 36 + 64 = 100, c = 10. This is the 3-4-5 triple times 2.
2
B) 12 cm
a² + 5² = 13². a² + 25 = 169. a² = 144. a = 12. This is the 5-12-13 triple.
3
B) 5 units
Horizontal: 6-2=4, Vertical: 6-3=3. 4² + 3² = 16 + 9 = 25, c = 5.
4
Select: 5-12-13, 8-15-17, 7-24-25
5-12-13: 25 + 144 = 169 = 13² YES
4-5-6: 16 + 25 = 41 ≠ 36 NO
8-15-17: 64 + 225 = 289 = 17² YES
7-24-25: 49 + 576 = 625 = 25² YES
6-7-8: 36 + 49 = 85 ≠ 64 NO
5
B) 12 feet
The ladder (15) is the hypotenuse. 9² + h² = 15². 81 + h² = 225. h² = 144. h = 12.
6
B) 20 meters
12² + 16² = 144 + 256 = 400, c = 20. This is the 3-4-5 triple times 4.
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for 3D applications, converse theorem, and complex word problems.
4-5/6 Approaching Mastery Review specific area: identifying hypotenuse, finding legs, or distance formula.
2-3/6 Developing Reteach with visual models. Practice labeling triangles before solving. Use Pythagorean triples for confidence.
0-1/6 Needs Intervention Small group instruction. Review squares and square roots. Use manipulatives to show the relationship visually.
FAST Success Kit | Grade 8 | FL B.E.S.T. Standards: MA.8.GR.1.1, MA.8.GR.1.2, MA.8.GR.1.3 | Answer Key - Teacher Use Only