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Year 10 Maths — Similar triangles

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

Name: ________________________

  1. 1.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
    • 1:25
    • 4:9
    • 1:9
    • 1:4

  2. 2.Are any two squares similar to each other?

    • a) No, never
    • b) Only if they are the same size
    • c) Only if they are drawn on grid paper
    • d) Yes, always

  3. 3.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?

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

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

  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.The Basic Proportionality Theorem says that a line drawn parallel to one side of a triangle...

    • a) divides the other two sides in the same ratio
    • b) cuts the other two sides exactly in half
    • c) makes the triangle isosceles
    • d) is equal in length to the side it is parallel to

  7. 7.Two similar triangles have sides in the ratio 1:4. The area of the smaller is 5 square centimetres. What is the area of the larger, in square centimetres?

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

    Groups: Always similar · Not always similar

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

Answer key — Year 10 Maths — Similar triangles

  1. 1. 1:2 → 1:4; 1:3 → 1:9; 2:3 → 4:9; 3:4 → 9:16; 1:5 → 1:25
  2. 2. d) Yes, always
  3. 3. 30
  4. 4. b) similar
  5. 5. 15
  6. 6. a) divides the other two sides in the same ratio
  7. 7. 80
  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