Pythagorean Theorem practice worksheet with multiple-choice questions and a diagram of a right triangle.

Let’s go through each question one by one, step by step.

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Question 1: Which set of sides would make a right triangle?

We use the Pythagorean Theorem:
For a right triangle, a² + b² = c², where c is the longest side (hypotenuse).

Check each option:

- A: 5, 12, 13 → 5² + 12² = 25 + 144 = 169 → 13² = 169 → ✔ YES!
- B: 8, 10, 12 → 8² + 10² = 64 + 100 = 164 → 12² = 144 → ✘ No
- C: 5, 10, 12 → 5² + 10² = 25 + 100 = 125 → 12² = 144 → ✘ No
- D: 4, 5, 6 → 4² + 5² = 16 + 25 = 41 → 6² = 36 → ✘ No

✔ Only A works.

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Question 2: a² + b² = c², a = 9, b = 40 → find c

Plug in:
9² + 40² = 81 + 1600 = 1681
Now take square root of 1681 → √1681 = 41

So c = 41

✔ Answer: C

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Question 3: a² + b² = c², b = 35, c = 37 → find a

Rearrange: a² = c² - b²
a² = 37² - 35² = 1369 - 1225 = 144
√144 = 12

So a = 12

✔ Answer: C

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Question 4: Right triangle with legs 5 and 4, find hypotenuse c

Use Pythagoras:
c² = 5² + 4² = 25 + 16 = 41
c = √41 ≈ 6.4 (since 6.4² = 40.96 — very close)

Looking at options:
A: 3 → too small
B: 6.4 → matches approximation
C: 41 → that’s c², not c
D: 9 → too big

✔ Answer: B (6.4)

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Question 5: Side “a” on a right triangle is ALWAYS the longest side

No! In the formula a² + b² = c², c is always the hypotenuse — the longest side. “a” and “b” are the legs — they can be any length, as long as they’re shorter than c.

Also, sometimes people label sides differently — but conventionally, c is the hypotenuse.

So saying “side a is ALWAYS the longest” is FALSE.

✔ Answer: A (false)

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Question 6: What is the longest side of a right triangle called?

It’s called the hypotenuse.

Legs are the other two sides.

“Pythagoras’ Big Buddy” is funny, but not real 😄

✔ Answer: D (Hypotenuse)

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Final Answer:
1. A
2. C
3. C
4. B
5. A
6. D