Lesson G5

G5 Congruence criteria for triangles (SSS, SAS, ASA, RHS) Quiz: AQA Maths, Unit 4

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson G5, Congruence criteria for triangles (SSS, SAS, ASA, RHS): 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. Which of these is a valid congruence criterion for triangles?

    • LLL
    • AAA
    • SSS
    • SSA

  2. What does the SAS criterion mean?

    • Two sides and any one angle are equal in size
    • Two angles and any one side are equal
    • Two sides and the included angle are equal
    • One side and two angles are equal in the triangles

  3. Which congruence criterion applies to two right-angled triangles?

    • SAS
    • AAA
    • RHS
    • SSA

  4. What does the ASA criterion mean?

    • One angle and two sides not included are equal
    • Two angles and the included side are equal
    • Two sides and one angle are equal
    • Two angles and any side are equal

  5. Which set of information proves two triangles are congruent?

    • Three angles of one equal to three angles of the other
    • Two sides and an angle not between them equal
    • Two angles and no sides equal
    • Three sides of one equal to three sides of the other

  6. Two triangles have all three angles equal. Are they necessarily congruent?

    • Yes, because all angles are equal
    • No, they may be similar but of different sizes
    • Yes, because they have the same shape
    • No, because the angle sums are different

  7. Triangles ABC and DEF have AB = DE = 5 cm, BC = EF = 7 cm and angle B = angle E = 40 degrees. Which criterion proves congruence?

    • RHS
    • ASA
    • SAS
    • SSS

  8. Two triangles each have an angle of 30 degrees and an angle of 70 degrees, with the 6 cm side between those two angles in both. Which criterion applies?

    • ASA
    • AAA
    • SSS
    • SAS

  9. Two right-angled triangles have a hypotenuse of 10 cm and another side of 6 cm. Which criterion proves they are congruent?

    • RHS
    • SAS
    • SSA
    • AAA

  10. Which of these is NOT a congruence criterion for triangles?

    • SAS
    • ASA
    • AAA
    • SSS

  11. Triangles with sides 3, 4, 5 cm and 6, 8, 10 cm are compared. Are they congruent?

    • Yes, by RHS
    • Yes, by SSS
    • No, because one has a right angle and the other does not
    • No, they are similar but not congruent

  12. Triangle PQR has PQ = 8 cm, QR = 6 cm and angle Q = 35 degrees. Triangle XYZ has XY = 8 cm, YZ = 6 cm and angle Y = 35 degrees. Which criterion applies?

    • RHS
    • ASA
    • SAS
    • SSS

  13. How many pairs of equal sides are needed to prove congruence by SSS?

    • 3 pairs of sides
    • 2 pairs of sides and 1 angle
    • 2 pairs of angles and 1 side
    • 3 pairs of angles

  14. Which congruence criterion uses a hypotenuse?

    • SSS
    • RHS
    • SAS
    • ASA

  15. Triangle ABC has sides 7 cm, 9 cm and 12 cm. Triangle DEF has sides 7 cm, 9 cm and 12 cm labelled differently. Are they congruent?

    • Yes, by SAS
    • No, because they are not right-angled
    • Yes, by SSS
    • No, because the labels differ

  16. In triangles ABC and DEF, AB = DE = 4 cm, AC = DF = 6 cm and angle A = angle D = 50 degrees. Which criterion applies?

    • SAS
    • RHS
    • ASA
    • SSS

  17. What must a congruence proof show?

    • Enough matching sides and angles to satisfy one of the four criteria
    • Equal angles only, so the two triangles are similar shapes
    • Equal perimeters, as long as one pair of sides matches
    • Equal areas and equal perimeters for both shapes only

  18. Two isosceles triangles have a base of 10 cm and base angles of 40 degrees. Are they congruent?

    • Yes, by ASA
    • No, because isosceles triangles are never congruent
    • No, because the apex angles are unknown
    • Yes, by SSS

  19. What must be true of the angle used in an SAS congruence proof?

    • It sits between the two equal sides
    • It lies outside both equal sides
    • It is always 90 degrees
    • It is opposite the longest side

  20. Which information alone does not guarantee congruence?

    • A right angle, hypotenuse and one other side equal
    • Three equal sides
    • Two equal angles and an equal side between them
    • Three equal angles

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