Right triangles

Pythagoras, and the two lengths the altitude to the hypotenuse hands you — the altitude itself, and a leg from the whole.

3 sheets · 24 questions · one answer key · 4 pages

Recommended for grades 9–10

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Pythagoras Sheet 1 of 3

PythagorasBoth directions

Name: Date:

Find the missing side. All lengths are in centimeters.

1 cm

2 cm

3 cm

4 cm

5 cm

6 cm

7 cm

8 cm

Altitude to the hypotenuseThe altitude

Name: Date:

Find each altitude. The altitude is the geometric mean of the two pieces.

1h =

2h =

3h =

4h =

5h =

6h =

7h =

8h =

Altitude to the hypotenuseA leg

Name: Date:

Find each leg. A leg is the geometric mean of the hypotenuse and its piece.

1a =

2a =

3a =

4a =

5a =

6a =

7a =

8a =

Power Pack · Right trianglesAnswer key

Pythagoras

1. 15, 36, 39 — hypotenuse: 39 cm2. 12, 16, 20 — leg: 16 cm3. 6, 8, 10 — leg: 8 cm4. 6, 8, 10 — hypotenuse: 10 cm5. 3, 4, 5 — leg: 4 cm6. 7, 24, 25 — hypotenuse: 25 cm7. 12, 35, 37 — leg: 35 cm8. 9, 12, 15 — hypotenuse: 15 cm

The altitude to the hypotenuse

1. h² = p × q = 12 × 27 → h = 182. h² = p × q = 4 × 9 → h = 63. h² = p × q = 8 × 18 → h = 124. h² = p × q = 9 × 9 → h = 95. h² = p × q = 5 × 5 → h = 56. h² = p × q = 18 × 32 → h = 247. h² = p × q = 2 × 8 → h = 48. h² = p × q = 16 × 16 → h = 16

A leg from the hypotenuse

1. a² = c × q = 25 × 16 → a = 202. a² = c × q = 8 × 2 → a = 43. a² = c × q = 20 × 5 → a = 104. a² = c × q = 25 × 9 → a = 155. a² = c × q = 32 × 8 → a = 166. a² = c × q = 9 × 4 → a = 67. a² = c × q = 32 × 18 → a = 248. a² = c × q = 27 × 12 → a = 18

Right triangles

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