# 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.