Pythagoras’ theorem
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Log in to continueFind unknown right-triangle side lengths and check which side is the hypotenuse.
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Find the length of BC, the hypotenuse.
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Right triangle ABC has a right angle at A, AB = 3 cm and AC = 4 cm.
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Answer: 5 cm
- BC² = 3² + 4² = 25.
- Take the positive square root: BC = 5 cm. It is longer than either other side.
- (3)^2 = 9.
- (4)^2 = 16.
- 9 + 16 = 25.
- √(25) = 5.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Find unknown right-triangle side lengths and check which side is the hypotenuse.
Read the official VCAA curriculum description (VC2M8M06)
These quizzes practise concepts within this topic. Multiple-choice answers alone do not demonstrate drawing, conducting an investigation or using a digital tool.
- VC2M8M06-C01Apply Pythagoras’ theorem to find a hypotenuse.
- VC2M8M06-C02Rearrange Pythagoras’ theorem to find a shorter side.
- VC2M8M06-C03Apply and explain pythagoras’ theorem using read and connect representations.
- VC2M8M06-C04Apply and explain pythagoras’ theorem using calculate and explain each step.
- VC2M8M06-C05Apply and explain pythagoras’ theorem using build and check a model.
- VC2M8M06-C06Apply and explain pythagoras’ theorem using work backwards from what is known.
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Subskills
These practice subskills map to the curriculum topic. Guided activities cover skills beyond multiple-choice questions.
Descriptor-derived subskills
- D01Add the two smaller squaresApply Pythagoras’ theorem to find a hypotenuse.
- D02Subtract before square-rootingRearrange Pythagoras’ theorem to find a shorter side.
- D03Read and connect representationsApply and explain pythagoras’ theorem using read and connect representations.
- D04Calculate and explain each stepApply and explain pythagoras’ theorem using calculate and explain each step.
- D05Build and check a modelApply and explain pythagoras’ theorem using build and check a model.
- D06Work backwards from what is knownApply and explain pythagoras’ theorem using work backwards from what is known.