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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