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

    Groups: Must be congruent · Need not be congruent

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

  2. 2.Two figures are congruent when they...

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

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

  5. 5.Two line segments are congruent when...

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

  6. 6.Triangle ABC is congruent to triangle PQR, with A matching P, B matching Q and C matching R. Tap the side of triangle PQR that matches side AB.

    Write the number of the part.

    123

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

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

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

Answer key — Year 8 Maths — Congruence

  1. 1. 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
  2. 2. b) have exactly the same shape and exactly the same size
  3. 3. 26
  4. 4. 72
  5. 5. c) they are the same length
  6. 6. 1 — PQ
  7. 7. 9
  8. 8. a) Yes — turning a shape changes neither its shape nor its size