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Year 9 Maths — Similar triangles

Use equal angles and side ratios in similar triangles, including the ratio of their areas.

Name: ________________________

  1. 1.Which of these is true of two similar triangles?

    • a) They must be the same size
    • b) They must be right-angled
    • c) Matching sides are in the same ratio
    • d) Matching sides are equal

  2. 2.Two similar triangles have sides in the ratio 2:3. The area of the smaller is 16 square centimetres. What is the area of the larger, in square centimetres?

  3. 3.Two similar triangles have sides in the ratio on the left. Match it to the ratio of their areas.

    • 1:2
    • 1:3
    • 2:3
    • 3:4
    • 1:5
    • 9:16
    • 4:9
    • 1:9
    • 1:25
    • 1:4

  4. 4.Two similar triangles have sides in the ratio 3:5. The perimeter of the smaller is 18 cm. What is the perimeter of the larger, in centimetres?

  5. 5.Triangle ABC is similar to triangle PQR. AB is 4 cm and PQ is 12 cm. BC is 5 cm. How long is QR, in centimetres?

  6. 6.Two triangles have all three pairs of angles equal. The triangles are...

    • a) congruent
    • b) always right-angled
    • c) similar
    • d) unrelated

  7. 7.A 2 m pole casts a shadow 3 m long. At the same moment a tree casts a shadow 18 m long. How tall is the tree, in metres?

  8. 8.Sort each pair of shapes by whether they must always be similar.

    Groups: Always similar · Not always similar

    • Two rectangles
    • Two isosceles triangles
    • Two rhombuses
    • Two equilateral triangles
    • Two squares
    • Two circles

Answer key — Year 9 Maths — Similar triangles

  1. 1. c) Matching sides are in the same ratio
  2. 2. 36
  3. 3. 1:2 → 1:4; 1:3 → 1:9; 2:3 → 4:9; 3:4 → 9:16; 1:5 → 1:25
  4. 4. 30
  5. 5. 15
  6. 6. c) similar
  7. 7. 12
  8. 8. Two squares → Always similar; Two circles → Always similar; Two equilateral triangles → Always similar; Two rectangles → Not always similar; Two isosceles triangles → Not always similar; Two rhombuses → Not always similar