Practice worksheet for identifying right triangles using the Pythagorean theorem.

Let’s solve each part step by step.

We’re checking if triangles are right triangles.
A right triangle has one 90-degree angle, and it follows the Pythagorean Theorem:
> In a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides.
> That is: a² + b² = c², where c is the longest side.

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Part A) Check each triangle:

#### 1) Sides: 8 ft, 15 ft, 17 ft
Longest side = 17 → check if 8² + 15² = 17²
8² = 64
15² = 225
64 + 225 = 289
17² = 289 → ✔ YES, it’s a right triangle.

#### 2) Sides: 7 yd, 11 yd, 18 yd
Longest side = 18 → check if 7² + 11² = 18²
7² = 49
11² = 121
49 + 121 = 170
18² = 324 → 170 ≠ 324 → ✘ NOT a right triangle.

#### 3) Sides: 4 in, 6 in, 9 in
Longest side = 9 → check if 4² + 6² = 9²
4² = 16
6² = 36
16 + 36 = 52
9² = 81 → 52 ≠ 81 → ✘ NOT a right triangle.

#### 4) Sides: 10 ft, 24 ft, 26 ft
Longest side = 26 → check if 10² + 24² = 26²
10² = 100
24² = 576
100 + 576 = 676
26² = 676 → ✔ YES, it’s a right triangle.

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Part B) Word problems:

#### 1) Triangle with sides 25 yd, 13 yd, 16 yd
Longest side = 25 → check if 13² + 16² = 25²
13² = 169
16² = 256
169 + 256 = 425
25² = 625 → 425 ≠ 625 → ✘ NOT a right triangle → Answer: b) No

#### 2) Triangle with sides 4 ft, 3 ft, 5 ft
Longest side = 5 → check if 3² + 4² = 5²
3² = 9
4² = 16
9 + 16 = 25
5² = 25 → ✔ YES, it’s a right triangle → Answer: a) Yes

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Final Answer:
A)
1) Yes
2) No
3) No
4) Yes

B)
1) b) No
2) a) Yes