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Grade 10 Math — 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
    • 1:25
    • 9:16
    • 1:9
    • 1:4
    • 4:9

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

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

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

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

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

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

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

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

    Groups: Always similar · Not always similar

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

  8. 8.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

Answer key — Grade 10 Math — 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. 12
  3. 3. 30
  4. 4. d) divides the other two sides in the same ratio
  5. 5. d) Matching sides are in the same ratio
  6. 6. 36
  7. 7. 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
  8. 8. d) Yes, always