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studyGeometry & Mensuration
CoreMaths revision

Pythagoras’ Theorem

Use right-triangle structure for lengths, coordinates and converse reasoning.

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Focus points
✓Find missing sides in right triangles.
✓Use the converse of Pythagoras.
✓Apply distance reasoning.
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The Wise Owl

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target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · Pythagoras
A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · Pythagoras
A right triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · rectangle diagonal
Find the diagonal of a rectangle 8 cm by 15 cm.
Question 4FluencyCore
Original practice · Free Online Revision
Skill · converse
Determine whether sides 7,24,25 form a right triangle.
Question 5FluencyCore
Original practice · Free Online Revision
Skill · coordinate distance
Find the distance between (−2,3) and (4,11).
Question 6ApplicationCore
Original practice · Free Online Revision
Skill · application
A 10 m ladder reaches 8 m up a wall. How far is its foot from the wall?
Question 7ReasoningStretch
Original practice · Free Online Revision
Skill · triangle classification
A triangle has side lengths 6,8,11. Is it acute, right or obtuse?
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · square diagonal
A square has diagonal 10 cm. Find its exact area.