Year 10 Maths — Similar triangles

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

Name: ________________________

1.Which of these is true of two similar triangles?
- a) Matching sides are equal
- b) They must be right-angled
- c) Matching sides are in the same ratio
- d) They must be the same size
2.Are any two squares similar to each other?
- a) No, never
- b) Only if they are drawn on grid paper
- c) Yes, always
- d) Only if they are the same size
3.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) is equal in length to the side it is parallel to
- c) divides the other two sides in the same ratio
- d) makes the triangle isosceles
4.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?
5.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?
6.Two triangles have all three pairs of angles equal. The triangles are...
- a) congruent
- b) always right-angled
- c) similar
- d) unrelated
7.Sort each pair of shapes by whether they must always be similar.
Groups: Always similar · Not always similar
- Two rhombuses
- Two rectangles
- Two circles
- Two squares
- Two isosceles triangles
- Two equilateral triangles
8.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?

Answer key — Year 10 Maths — Similar triangles

1. c) Matching sides are in the same ratio
2. c) Yes, always
3. c) divides the other two sides in the same ratio
4. 36
5. 6
6. c) similar
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. 30