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

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

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

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

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

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

  6. 6.Triangle PQR is congruent to triangle XYZ. Angle X is 40° and angle Y is 65°. How big is angle R, in degrees?

  7. 7.Triangle LMN is congruent to triangle XYZ. Match each part of LMN to the part of XYZ that matches it.

    • side LM
    • side MN
    • side LN
    • angle L
    • angle N
    • side XY
    • side XZ
    • angle X
    • side YZ
    • angle Z

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

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

Answer key — Year 7 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. c) have exactly the same shape and exactly the same size
  3. 3. 9
  4. 4. b) Yes — turning a shape changes neither its shape nor its size
  5. 5. 72
  6. 6. 75
  7. 7. side LM → side XY; side MN → side YZ; side LN → side XZ; angle L → angle X; angle N → angle Z
  8. 8. a) they are the same length