Pythagorean Theorem Practice Worksheet

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📐 Part 1: Finding Missing Sides (Easy to Moderate)

1. In a right triangle, if a = 3 cm and b = 4 cm, find the hypotenuse c.

Answer: c = ________ cm

2. The hypotenuse of a right triangle is 13 cm and one side is 5 cm. Find the other side.

Answer: ________ cm

3. A ladder 10 metres long is placed against a wall. The foot of the ladder is 6 metres from the wall. How high up the wall does the ladder reach?

Answer: ________ metres

4. In triangle ABC, ∠B = 90°, AB = 8 cm, BC = 15 cm. Find AC.

Answer: AC = ________ cm

5. Check whether the following sets of numbers form a Pythagorean triplet:

a) 7, 24, 25

Answer: ________ (Yes/No)

b) 9, 12, 16

Answer: ________ (Yes/No)

6. In triangle PQR, PQ = 12 cm, QR = 16 cm, PR = 20 cm. Prove that triangle PQR is a right triangle and identify the right angle.

7. Advanced: In a right triangle, one side is 2 cm longer than the other side, and the hypotenuse is 10 cm. Find the lengths of the two sides.

Shorter side = ________ cm, Longer side = ________ cm

8. A rectangular field is 40 metres long and 30 metres wide. Find the length of its diagonal.

Answer: ________ metres

9. Extension Activity: A man walks 12 km north, then 5 km east. How far is he from his starting point?

Distance from starting point = ________ km

10. Challenge: In an isosceles right triangle, each equal side is 8 cm. Find the hypotenuse and verify using Pythagorean theorem.

Hypotenuse = ________ cm

Success Criteria:

✓ I can apply the Pythagorean theorem: a² + b² = c²

✓ I can find missing sides in right triangles

✓ I can verify Pythagorean triplets

✓ I can solve real-world problems using the theorem

Differentiation Note: Questions 1-4 are foundational, 5-7 are intermediate, 8-10 are advanced with extension opportunities.