# Lesson Worksheet: Triangle Similarity Criteria and Their Applications Mathematics

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

**Q3: **

If , evaluate .

- A97
- B
- C
- D

**Q5: **

Given that and are similar, find the length .

**Q7: **

Triangles and are similar.

Work out the length of .

Work out the length of .

**Q9: **

Find the value of rounded to the nearest hundredth.

**Q11: **

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

**Q12: **

In the figure, suppose also that , and that . What is the length of ?

**Q16: **

Find the length of and round the result to the nearest tenth.

**Q18: **

The figure shows triangles and .

Work out the value of .

- A
- B7
- C5
- D
- E15

Work out the value of .

Work out the value of .

- A8
- B
- C6
- D
- E

**Q20: **

In the figure, given that , , , and , find the lengths of each of and .

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

**Q21: **

Triangles and are similar.

Work out the value of .

Work out the value of .

**Q22: **

In the figure, suppose that . Determine the lengths of and to two decimal places.

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

**Q23: **

Given that the shown triangles are similar, determine the length of . Give your answer to one decimal place if necessary.

**Q24: **

Triangles and are similar.

Work out the value of .

- A
- B
- C3
- D
- E

Work out the value of .

- A
- B3
- C
- D
- E

**Q25: **

In the given figure, lies on both and . and each have a length of 4, and has a length of 3.

Calculate the length of .

- A
- B5
- C4
- D3
- E

Calculate the length of .

Hence, calculate the length of .

- A
- B1
- C
- D3
- E4