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Grade 8 Math — 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.In the statement 'triangle ABC is congruent to triangle PQR', which side matches AB?

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

  2. 2.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

  3. 3.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

  4. 4.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

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

  6. 6.Triangle ABC is congruent to triangle DEF. BC is 9 inches long. How long is EF, in inches?

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

  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) No, because it is facing a different way
    • c) Only if it is turned back first
    • d) Only if it was the right way up to begin with

Answer key — Grade 8 Math — Congruence

  1. 1. d) PQ
  2. 2. side LM → side XY; side MN → side YZ; side LN → side XZ; angle L → angle X; angle N → angle Z
  3. 3. c) have exactly the same shape and exactly the same size
  4. 4. 1 — PQ
  5. 5. Two squares with sides of 4 inches → Must be congruent; Two rectangles with the same area → Need not be congruent; Two equilateral triangles with sides of 5 inches → Must be congruent; Two triangles with the same three angles → Need not be congruent; Two line segments 7 inches long → Must be congruent; Two rectangles with the same perimeter → Need not be congruent
  6. 6. 9
  7. 7. 72
  8. 8. a) Yes — turning a shape changes neither its shape nor its size