Lesson G6

G6 Geometric reasoning, simple proofs and Pythagoras' theorem Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G6, Geometric reasoning, simple proofs and Pythagoras' theorem: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 4: Geometry and measures, written with Revision Ninja.

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The 20 questions

  1. A right-angled triangle has legs of 6 cm and 8 cm. What is the hypotenuse?

    • 48 cm
    • 14 cm
    • 100 cm
    • 10 cm

  2. Why is the hypotenuse the longest side of a right-angled triangle?

    • It is opposite the largest angle, the right angle
    • It is always twice the length of the shortest side
    • It is always the diagonal of a square drawn on the base
    • It is always the base, so it is drawn along the bottom

  3. A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. What is the other leg?

    • 169
    • 18
    • 12
    • 8

  4. In Pythagoras' theorem a² + b² = c², what does c represent?

    • A shorter side
    • The perpendicular height
    • Any side of the triangle
    • The hypotenuse

  5. Does a triangle with sides 5, 12 and 13 have a right angle?

    • Yes, because 5² + 12² = 13²
    • No, because 5 + 12 is not 13
    • No, because 13 is not an even number
    • Yes, because all sides are whole numbers

  6. A right-angled triangle has legs of 3 cm and 4 cm. What is its hypotenuse?

    • 5 cm
    • 25 cm
    • 7 cm
    • 12 cm

  7. A triangle has two equal sides. Which fact must be true about its base angles?

    • They are both right angles
    • They are equal
    • They add up to 180 degrees
    • They are double the apex angle

  8. A proof that the angles in a triangle sum to 180 degrees draws a line parallel to one side. Which fact is then used?

    • Angles around a point sum to 360 degrees
    • Vertically opposite angles are not equal
    • Alternate angles on parallel lines are equal
    • Diagonals of a rectangle bisect each other

  9. A quadrilateral is split into two triangles by a diagonal. What does this show about its angle sum?

    • 360 degrees
    • 540 degrees
    • 720 degrees
    • 180 degrees

  10. A rectangle measures 9 cm by 12 cm. What is its diagonal?

    • 21 cm
    • 15 cm
    • 108 cm
    • 10.5 cm

  11. A right-angled triangle has a hypotenuse of 10 cm and one leg of 6 cm. What is the other leg?

    • 8 cm
    • 4 cm
    • 16 cm
    • 64 cm

  12. A square has sides of 4 cm. What is its diagonal, in exact form?

    • 16 cm
    • 2√2 cm
    • 8 cm
    • 4√2 cm

  13. A 10 m ladder reaches 8 m up a wall. How far is its foot from the wall?

    • 2 m
    • 12 m
    • 6 m
    • 18 m

  14. Is a triangle with sides 8 cm, 15 cm and 17 cm right-angled?

    • No, since 8² + 15² = 16²
    • No, since 8 + 15 is greater than 17 only in cases of right angles
    • No, since 17 is the largest side
    • Yes, since 8² + 15² = 17²

  15. Why must a triangle with three angles of 60 degrees have equal sides?

    • Equal angles in a triangle mean equal sides
    • Equal angles always make a circle
    • Equal angles mean the triangle is scalene
    • Equal angles give a right-angled triangle

  16. Which angle facts prove that an exterior angle of a triangle equals the sum of the two opposite interior angles?

    • Vertically opposite angles are equal and the exterior angle is 90 degrees
    • Angles around a point sum to 360 degrees, and opposite angles are equal
    • Angles on a straight line sum to 180 degrees and the triangle sums to 180 degrees
    • Corresponding angles on a transversal are equal, and the triangle sums to 360 degrees

  17. A rectangle has a diagonal of 25 cm and one side of 7 cm. What is the other side?

    • 18 cm
    • 24 cm
    • 576 cm
    • 32 cm

  18. A right-angled isosceles triangle has legs of length x. What is its hypotenuse?

    • x√2
    • x/√2
    • x²√2
    • 2x

  19. A triangle has sides 9 cm, 12 cm and 14 cm. Is it right-angled?

    • Yes, because 9 + 12 is greater than 14
    • No, because 9² + 12² is not equal to 14²
    • No, because it has no right angle drawn
    • Yes, because 9² + 12² = 15²

  20. An isosceles triangle has a base of 10 cm and equal sides of 13 cm. What is its height?

    • 23 cm
    • 12 cm
    • 8 cm
    • 11.5 cm

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