← Back to the activity

Class 10 Maths — Similar triangles

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

Name: ________________________

  1. 1.In triangle ABC, DE is parallel to BC. AD is 2 cm, DB is 4 cm and AE is 3 cm. How long is EC, in centimetres?

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

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

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

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

  4. 4.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?

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

    Groups: Always similar · Not always similar

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

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

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

  7. 7.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?

  8. 8.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
    • 1:25
    • 1:4
    • 9:16
    • 4:9
    • 1:9

Answer key — Class 10 Maths — Similar triangles

  1. 1. 6
  2. 2. c) Yes, always
  3. 3. d) Matching sides are in the same ratio
  4. 4. 80
  5. 5. 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
  6. 6. b) divides the other two sides in the same ratio
  7. 7. 30
  8. 8. 1:2 → 1:4; 1:3 → 1:9; 2:3 → 4:9; 3:4 → 9:16; 1:5 → 1:25