# Lesson Worksheet: Triangle Similarity Criteria and Their Applications Mathematics

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

Q1:

Given that , , and , find the length of . Q2:

In the given figure, and are parallel. Use similarity to work out the value of . • A
• B
• C
• D
• E

Q3:

If , evaluate . • A97
• B
• C
• D

Q4:

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

Q5:

Given that and are similar, find the length . Q6:

Triangles and are similar. Work out the value of .

Work out the value of .

• A
• B
• C
• D6
• E7

Q7:

Triangles and are similar. Work out the length of .

Work out the length of .

Q8:

Triangles and are similar. Work out the measure of angle .

Work out the value of .

Work out the value of .

Q9:

Find the value of rounded to the nearest hundredth. Q10:

Triangles and are similar. Find to the nearest integer. Q11:

Given that , , , and , find the length of . Q12:

In the figure, suppose also that , and that . What is the length of ? Q13:

If , find and the length of to the nearest tenth. • A, 23.4 cm
• B, 19 cm
• C, 23.4 cm
• D, 15 cm

Q14:

In the figure, is similar to . If and , what is ? Q15:

is a rectangle in which , , and . Calculate the perimeter of . Q16:

Find the length of and round the result to the nearest tenth. Q17:

If , determine the length of rounded to the nearest hundredth, if necessary. 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

Q19:

In trapezoid , sides and are parallel, and its diagonals intersect at . Given that , , and , what is the length of ? 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