# 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:

The figure shows a triangle where the line segment is parallel to Which angle is equivalent to ? Give reasons.

• A, because the angles are corresponding.
• B, because the angles are corresponding.
• C, because the angles are corresponding.
• D, because the angles are alternate.
• E, because the angles are alternate.

Which angle is equivalent to ? Give reasons.

• A, because the angles are corresponding.
• B, because the angles are corresponding.
• C, because the angles are corresponding.
• D, because the angles are alternate.
• E, because the angles are alternate.

Hence, are triangles and similar? If yes, state why?

• AYes, they are similar by the SAS criterion.
• BNo
• CYes, they are similar by the AA criterion.
• DYes, they are similar by the SSS criterion.

Q2:

The figure shows two triangles and where the line segment is parallel to . Which angle is equivalent to ? Give reasons.

• A, because the angles are alternate
• B, because the angles are corresponding
• C, because the angles are corresponding
• D, because the angles are vertically opposite
• E, because the angles are alternate

Which angle is equivalent to ? Give reasons.

• A, because the angles are corresponding
• B, because the angles are alternate
• C, because the angles are alternate
• D, because the angles are corresponding
• E, because the angles are vertically opposite

Hence, are triangles and similar? If yes, state why.

• ANo
• BYes, they are similar by the SSS criterion.
• CYes, they are similar by the AA criterion.
• DYes, they are similar by the SAS criterion.

Q3:

In the figure, and . Since triangles and are similar, what is the scale factor? Q4:

In trapezoid , sides and are parallel, and its diagonals intersect at . Given that , , and , what is the length of ? Q5:

The figure shows triangle . Work out the value of .

Work out the value of .

Work out the perimeter of .

Q6:

The given figure shows a right triangle , where is perpendicular to . Using similarity, express in terms of and .

• A
• B
• C
• D
• E

Using similarity, express in terms of and .

• A
• B
• C
• D
• E

Express the sum of and in terms of .

• A
• B
• C
• D
• E

Q7:

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

Q8:

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

Q9:

Triangles and are similar. Find to the nearest integer. Q10:

A 1.97-meter-tall man stands 3.49 m away from a streetlight and casts a shadow that is 2.73 m long. How high is the lamp? Round your answer to the nearest tenth.

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