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 𝐷𝐸=74m, 𝐸𝐵=32m, and 𝐸𝐴=48m, find the length of 𝐶𝐴.

Q2:

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

Q3:

If 𝐴𝐵𝐶𝐴𝐷𝐸, evaluate 𝑥.

  • A97
  • B3113
  • C717
  • D7311

Q4:

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

  • Ano
  • Byes

Q5:

Given that 𝐴𝐵𝐶 and 𝐷𝐸𝐹 are similar, find the length 𝐷𝐻.

Q6:

Triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar.

Work out the value of 𝑥.

Work out the value of 𝑦.

  • A503
  • B353
  • C215
  • D6
  • E7

Q7:

Triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar.

Work out the length of 𝐴𝐶.

Work out the length of 𝐵𝐶.

Q8:

Triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar.

Work out the measure of angle 𝑥.

Work out the value of 𝑦.

Work out the value of 𝑧.

Q9:

Find the value of 𝑥 rounded to the nearest hundredth.

Q10:

Triangles 𝐴𝐵𝐶 and 𝐴𝐷𝐸 are similar. Find 𝑥 to the nearest integer.

Q11:

Given that 𝐸𝐷=10cm, 𝐴𝐸=8cm, 𝐸𝐶=20cm, and 𝐵𝐷=15cm, find the length of 𝐵𝐶.

Q12:

In the figure, suppose also that 𝐹𝑁=𝐷𝑁=2, and that 𝐵𝐹=1. What is the length of 𝐶𝐸?

Q13:

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

Q14:

In the figure, 𝐴𝐸𝐷 is similar to 𝐴𝐷𝐵. If 𝑚𝐴𝐷𝐸=(3𝑥+5) and 𝑚𝐴𝐵𝐷=(4𝑥5), what is 𝑚𝐴𝐷𝐸?

Q15:

𝐴𝐵𝐶𝐷 is a rectangle in which 𝐴𝐷=21cm, 𝐴𝑋=9cm, and 𝑋𝑀=12cm. Calculate the perimeter of 𝑌𝑀𝐶.

Q16:

Find the length of 𝐸𝐵 and round the result to the nearest tenth.

Q17:

If 𝐸𝐶=19cm, determine the length of 𝐸𝐷 rounded to the nearest hundredth, if necessary.

Q18:

The figure shows triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶.

Work out the value of 𝑥.

  • A163
  • B7
  • C5
  • D203
  • E15

Work out the value of 𝑦.

Work out the value of 𝑧.

  • A8
  • B163
  • C6
  • D203
  • E152

Q19:

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?

Q20:

In the figure, given that 𝐶𝐴𝑍𝑋, 𝐴𝐵=8cm, 𝑌𝑍=21cm, and 𝑋𝑍=3𝐴𝐶, find the lengths of each of 𝑋𝑌 and 𝐵𝐶.

  • A𝑋𝑌=8cm, 𝐵𝐶=21cm
  • B𝑋𝑌=24cm, 𝐵𝐶=7cm
  • C𝑋𝑌=21cm, 𝐵𝐶=7cm
  • D𝑋𝑌=83cm, 𝐵𝐶=63cm

Q21:

Triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar.

Work out the value of 𝑥.

Work out the value of 𝑦.

Q22:

In the figure, suppose that 𝐷𝐸=15.1. Determine the lengths of 𝐷𝐵 and 𝐵𝐶 to two decimal places.

  • A𝐷𝐵=2.00, 𝐵𝐶=26.43
  • B𝐷𝐵=19.50, 𝐵𝐶=39.64
  • C𝐷𝐵=19.50, 𝐵𝐶=24.54
  • D𝐷𝐵=8.67, 𝐵𝐶=16.36

Q23:

Given that the shown triangles are similar, determine the length of 𝐴𝐵. Give your answer to one decimal place if necessary.

Q24:

Triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar.

Work out the value of 𝑥.

  • A310
  • B274
  • C3
  • D152
  • E103

Work out the value of 𝑦.

  • A152
  • B3
  • C103
  • D427
  • E274

Q25:

In the given figure, 𝐺 lies on both 𝐸𝐻 and 𝐷𝐹. 𝐴𝐵 and 𝐷𝐻 each have a length of 4, and 𝐺𝐷 has a length of 3.

Calculate the length of 𝐴𝐶.

  • A143
  • B5
  • C4
  • D3
  • E163

Calculate the length of 𝐹𝐺.

Hence, calculate the length of 𝐸𝐹.

  • A43
  • B1
  • C34
  • D3
  • E4

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