The portal has been deactivated. Please contact your portal admin.

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 𝐴𝐷𝐸 where the line segment 𝐵𝐶 is parallel to 𝐷𝐸

Which angle is equivalent to 𝐴𝐵𝐶? Give reasons.

  • A𝐴𝐶𝐵, because the angles are corresponding.
  • B𝐴𝐷𝐸, because the angles are corresponding.
  • C𝐴𝐸𝐷, because the angles are corresponding.
  • D𝐴𝐷𝐸, because the angles are alternate.
  • E𝐴𝐶𝐵, because the angles are alternate.

Which angle is equivalent to 𝐴𝐶𝐵? Give reasons.

  • A𝐴𝐵𝐶, because the angles are corresponding.
  • B𝐴𝐸𝐷, because the angles are corresponding.
  • C𝐴𝐷𝐸, because the angles are corresponding.
  • D𝐴𝐷𝐸, because the angles are alternate.
  • E𝐴𝐸𝐷, because the angles are alternate.

Hence, are triangles 𝐴𝐵𝐶 and 𝐴𝐷𝐸 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 𝐴𝐵𝐶 and 𝐷𝐸𝐶 where the line segment 𝐴𝐵 is parallel to 𝐷𝐸.

Which angle is equivalent to 𝐴𝐵𝐶? Give reasons.

  • A𝐶𝐸𝐷, because the angles are alternate
  • B𝐶𝐷𝐸, because the angles are corresponding
  • C𝐶𝐸𝐷, because the angles are corresponding
  • D𝐷𝐶𝐸, because the angles are vertically opposite
  • E𝐶𝐷𝐸, because the angles are alternate

Which angle is equivalent to 𝐵𝐴𝐶? Give reasons.

  • A𝐶𝐸𝐷, because the angles are corresponding
  • B𝐶𝐷𝐸, because the angles are alternate
  • C𝐶𝐸𝐷, because the angles are alternate
  • D𝐶𝐷𝐸, because the angles are corresponding
  • E𝐷𝐶𝐸, because the angles are vertically opposite

Hence, are triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐶 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, 𝐶𝐵=5.7 and 𝐵𝐸=9.12. Since triangles 𝐶𝐵𝐴 and 𝐸𝐵𝐷 are similar, what is the scale factor?

Q4:

In trapezoid 𝐴𝐵𝐶𝐷, sides 𝐴𝐷 and 𝐵𝐶 are parallel, and its diagonals intersect at 𝑀. Given that 𝐴𝐷=66, 𝐵𝐶=33, and 𝐴𝐶=75, what is the length of 𝑀𝐴?

Q5:

The figure shows triangle 𝐴𝐵𝐶.

Work out the value of 𝑥.

Work out the value of 𝑦.

Work out the perimeter of 𝐴𝐵𝐶.

Q6:

The given figure shows a right triangle 𝐴𝐵𝐶, where 𝐶𝐷 is perpendicular to 𝐴𝐵.

Using similarity, express 𝑎 in terms of 𝑐 and 𝑑.

  • A𝑎=𝑐𝑑
  • B𝑎=(𝑐𝑑)
  • C𝑎=𝑐𝑑
  • D𝑎=(𝑐𝑑)
  • E𝑎=𝑐𝑑

Using similarity, express 𝑏 in terms of 𝑐 and 𝑒.

  • A𝑏=𝑐𝑒
  • B𝑏=𝑐𝑒
  • C𝑏=𝑐𝑒
  • D𝑏=(𝑐𝑒)
  • E𝑏=(𝑐𝑒)

Express the sum of 𝑎 and 𝑏 in terms of 𝑐.

  • A𝑎+𝑏=𝑐2
  • B𝑎+𝑏=2𝑐
  • C𝑎+𝑏=𝑐
  • D𝑎+𝑏=𝑐
  • E𝑎+𝑏=2𝑐

Q7:

If 𝐴𝐵𝐷𝐴𝐶𝐵, find 𝑚𝐷𝐵𝐶 and the length of 𝐶𝐷 to the nearest tenth.

  • A71, 23.4 cm
  • B32, 19 cm
  • C39, 23.4 cm
  • D39, 15 cm

Q8:

In the given figure, 𝐷𝐸 and 𝐵𝐶 are parallel. Use similarity to work out the value of 𝑥.

  • A𝑥=68
  • B𝑥=3
  • C𝑥=1
  • D𝑥=6
  • E𝑥=5

Q9:

Triangles 𝐴𝐵𝐶 and 𝐴𝐷𝐸 are similar. Find 𝑥 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.

This lesson includes 115 additional questions and 693 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.