In this worksheet, we will practice using the properties of similar triangles to solve problems.

**Q3: **

In the given figure, and are parallel. Use similarity to work out the value of .

- A
- B
- C
- D
- E

**Q4: **

If , evaluate .

- A
- B97
- C
- D

**Q5: **

Given that , if 6 units are added to the length of each side, are the new triangles similar?

- Ano
- Byes

**Q7: **

Which of the following properties is enough to conclude that two triangles are similar?

- ATwo corresponding sides have the same ratio.
- BThey both contain a right angle.
- CAll corresponding angles have the same ratio.
- DThey have the same measure of angles.
- EOne corresponding side and one corresponding angle are equal.

**Q8: **

Fill in the blank: .

- A ,
- B ,
- C ,
- D ,

**Q10: **

is a right-angled triangle at . is a point on such that . If and , calculate the lengths of and . Round your answers to the nearest hundredth.

- A ,
- B ,
- C ,
- D ,

**Q11: **

Triangles and are similar.

Work out the value of .

Work out the value of .

- A
- B
- C7
- D6
- E

**Q12: **

Triangles and are similar.

Work out the length of .

Work out the length of .

**Q13: **

Triangle can be dilated by a scale factor of two onto triangle .

Determine the length of .

- A3
- B6
- C8
- D4

Determine the length of .

- A9
- B3
- C4
- D6

Find the size of angle .

- A
- B
- C

**Q14: **

Triangles and are similar.

Work out the size of angle .

- A
- B
- C
- D
- E

Work out the value of .

- A 7.5
- B6.4
- C8
- D6
- E3

Work out the value of .

- A1.5
- B4
- C1.6
- D3.6
- E2.5

**Q15: **

Given that is a square, , and , find .

**Q16: **

Find the value of rounded to the nearest hundredth, if needed.

**Q17: **

Triangles and are similar. Find to the nearest integer.

**Q18: **

Given that and the area of , find the area of .

**Q19: **

where and . If the area of , what is the area of ?

**Q20: **

The diagonal of a small square is of the length of the diagonal of a larger square.
If the area of the smaller square is 9 cm^{2}, what is the area of the larger square?

**Q21: **

where
and .
If the area of is 1,848 cm^{2}, what is the area of ?

**Q22: **

If the ratio between the sides of two similar polygons is , what is the ratio between their areas?

- A
- B
- C
- D
- E

**Q23: **

Square A is an enlargement of Square B by a scale factor of . If the perimeter of Square A equals 56 cm, what is the area of Square B? Give your answer to the nearest hundredth.

**Q24: **

It cost to fit wooden flooring in a class with dimensions 28 m and 10 m. How much would it cost to fit wooden flooring in a similar room with dimensions 84 m and 30 m.

**Q25: **

If , find the scale factor of similarity of to and the values of and .

- A scale factor, ,
- B scale factor, ,
- C scale factor, ,
- D scale factor, ,
- E scale factor, ,