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Year 8 Maths — Congruence

Say when two figures are congruent, read a congruence statement in the right order, and use it to find matching sides and angles.

Name: ________________________

  1. 1.Triangle ABC is congruent to triangle DEF. BC is 9 cm long. How long is EF, in centimetres?

  2. 2.Sort each pair of figures by whether they have to be congruent.

    Groups: Must be congruent · Need not be congruent

    • Two rectangles with the same area
    • Two line segments 7 cm long
    • Two triangles with the same three angles
    • Two rectangles with the same perimeter
    • Two squares with sides of 4 cm
    • Two equilateral triangles with sides of 5 cm

  3. 3.Triangle ABC is congruent to triangle PQR. The perimeter of ABC is 26 cm. What is the perimeter of PQR, in centimetres?

  4. 4.In the statement 'triangle ABC is congruent to triangle PQR', which side matches AB?

    • a) PQ
    • b) QR
    • c) AP
    • d) PR

  5. 5.Two figures are congruent when they...

    • a) have exactly the same shape and exactly the same size
    • b) have the same area as each other
    • c) have the same number of sides as each other
    • d) have the same shape, but may be different sizes

  6. 6.A square tile is lifted up and put back down turned a quarter turn. Is it congruent to the way it was before?

    • a) Only if it is turned back first
    • b) No, because it is facing a different way
    • c) Yes — turning a shape changes neither its shape nor its size
    • d) Only if it was the right way up to begin with

  7. 7.Triangle ABC is congruent to triangle DEF. Angle C is 72°. How big is angle F, in degrees?

  8. 8.Two line segments are congruent when...

    • a) they are both perfectly straight
    • b) they point in the same direction
    • c) they meet at a point
    • d) they are the same length

Answer key — Year 8 Maths — Congruence

  1. 1. 9
  2. 2. Two squares with sides of 4 cm → Must be congruent; Two rectangles with the same area → Need not be congruent; Two equilateral triangles with sides of 5 cm → Must be congruent; Two triangles with the same three angles → Need not be congruent; Two line segments 7 cm long → Must be congruent; Two rectangles with the same perimeter → Need not be congruent
  3. 3. 26
  4. 4. a) PQ
  5. 5. a) have exactly the same shape and exactly the same size
  6. 6. c) Yes — turning a shape changes neither its shape nor its size
  7. 7. 72
  8. 8. d) they are the same length