Worksheet: Similar Triangles

In this worksheet, we will practice using the properties of similar triangles to solve problems.

Q1:

These two rectangles are similar. Given that the area of the yellow one is 69.3 cm2, find the area of the green rectangle.

Q2:

Given that 𝐷𝐸=74m, 𝐸𝐡=32m, and 𝐸𝐴=48m, find the length of 𝐢𝐴.

Q3:

In the given figure, 𝐷𝐸 and 𝐡𝐢 are parallel. Use similarity to work out the value of π‘₯.

  • A π‘₯ = 6 8
  • B π‘₯ = 3
  • C π‘₯ = 1
  • D π‘₯ = 6
  • E π‘₯ = 5

Q4:

If β–³π΄π΅πΆβˆΌβ–³π΄π·πΈ, evaluate π‘₯.

  • A97
  • B 3 1 1 3
  • C 7 1 7
  • D 7 3 1 1

Q5:

Given that β–³πΉπΊπ»βˆΌβ–³π‘‹π‘Œπ‘, if 6 units are added to the length of each side, are the new triangles similar?

  • Ayes
  • Bno

Q6:

Find the value of π‘₯.

  • A 1 9 4
  • B2
  • C 2 5 4
  • D 7 2

Q7:

Which of the following properties is enough to conclude that two triangles are similar?

  • AAll corresponding angles have the same ratio.
  • BThey have the same measure of angles.
  • CTwo corresponding sides have the same ratio.
  • DThey both contain a right angle.
  • EOne corresponding side and one corresponding angle are equal.

Q8:

Fill in the blank: β–³π΄π΅πΆβˆΌβ–³βˆΌβ–³.

  • A 𝐷 𝐴 𝐢 , 𝐷 𝐡 𝐴
  • B 𝐷 𝐢 𝐴 , 𝐷 𝐴 𝐡
  • C 𝐴 𝐷 𝐢 , 𝐴 𝐷 𝐡
  • D 𝐢 𝐴 𝐷 , 𝐴 𝐡 𝐷

Q9:

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

Q10:

𝑋 π‘Œ 𝑍 is a right-angled triangle at 𝑋. 𝐿 is a point on π‘Œπ‘ such that οƒͺπ‘‹πΏβŸ‚π‘Œπ‘. If 𝑋𝑍=19cm and π‘‹π‘Œ=8cm, calculate the lengths of π‘ŒπΏ and 𝑋𝐿. Round your answers to the nearest hundredth.

  • A π‘Œ 𝐿 = 1 7 . 5 1 c m , 𝑋 𝐿 = 7 . 3 7 c m
  • B π‘Œ 𝐿 = 1 7 . 5 1 c m , 𝑋 𝐿 = 3 . 1 0 c m
  • C π‘Œ 𝐿 = 3 . 1 0 c m , 𝑋 𝐿 = 2 . 9 5 c m
  • D π‘Œ 𝐿 = 3 . 1 0 c m , 𝑋 𝐿 = 7 . 3 7 c m

Q11:

Triangles 𝐴𝐡𝐢 and 𝐴𝐡𝐢 are similar.

Work out the value of π‘₯.

Work out the value of 𝑦.

  • A 5 0 3
  • B 3 5 3
  • C 2 1 5
  • D6
  • E7

Q12:

Triangles 𝐴𝐡𝐢 and 𝐴′𝐡′𝐢′ are similar.

Work out the length of 𝐴𝐢.

Work out the length of 𝐡′𝐢′.

Q13:

Triangle 𝐴𝐡𝐢 can be dilated by a scale factor of two onto triangle 𝐴𝐡𝐢.

Determine the length of 𝐴′𝐡′.

Determine the length of 𝐴′𝐢′.

Find the measure of angle 𝐴′𝐡′𝐢′.

Q14:

Triangles 𝐴𝐡𝐢 and 𝐴𝐡𝐢 are similar.

Work out the measure of angle π‘₯.

Work out the value of 𝑦.

Work out the value of 𝑧.

Q15:

Given that π‘‹π‘Œπ‘πΏ is a square, π‘šβˆ π‘Œπ‘€π‘=(π‘˜+84)∘, and π‘šβˆ π‘€π‘Œπ‘=(π‘˜+33)∘, find π‘˜.

Q16:

Find the value of π‘₯ rounded to the nearest hundredth.

Q17:

Triangles 𝐴𝐡𝐢 and 𝐴𝐷𝐸 are similar. Find π‘₯ to the nearest integer.

Q18:

Given that 𝐴𝐷𝐷𝐢=37 and the area of △𝐴𝐡𝐢=484cm, find the area of △𝐴𝐷𝐸.

Q19:

𝐴 𝐡 𝐢 𝐷 𝐸 ∼ 𝐹 𝐺 𝐻 𝐾 𝑀 where 𝐴𝐢=46cm and 𝐹𝐻=11.5cm. If the area of 𝐴𝐡𝐢𝐷𝐸=3,036cm, what is the area of 𝐹𝐺𝐻𝐾𝑀?

Q20:

The diagonal of a small square is 34 of the length of the diagonal of a larger square. If the area of the smaller square is 9 cm2, what is the area of the larger square?

Q21:

𝐴 𝐡 𝐢 𝐷 ∼ 𝐸 𝐹 𝐺 𝐻 where 𝐴𝑁=7cm and 𝐸𝑀=2.8cm. If the area of 𝐴𝐡𝐢𝐷 is 1,848 cm2, what is the area of 𝐸𝐹𝐺𝐻?

Q22:

If the ratio between the sides of two similar polygons is 7∢6, what is the ratio between their areas?

  • A 7 ∢ 3
  • B 1 4 ∢ 3
  • C 7 ∢ 2
  • D 4 9 ∢ 3 6
  • E 7 ∢ 6

Q23:

Square A is an enlargement of Square B by a scale factor of 23. If the perimeter of Square A equals 56 cm, what is the area of Square B? Give your answer to the nearest hundredth.

Q24:

It cost 3,799pounds to fit wooden flooring in a class with dimensions 28 m and 10 m. How much would it cost to fit wooden flooring in a similar room with dimensions 84 m and 30 m.

Q25:

If 𝐴𝐡𝐢𝐷∼𝐸𝐹𝐺𝐻, find the scale factor of similarity of 𝐸𝐹𝐺𝐻 to 𝐴𝐡𝐢𝐷 and the values of 𝑋 and π‘Œ.

  • Ascale factor=25, 𝑋=13.6, π‘Œ=44
  • Bscale factor=425, 𝑋=5.44, π‘Œ=116
  • Cscale factor=12, 𝑋=85, π‘Œ=3.68
  • Dscale factor=25, 𝑋=44, π‘Œ=13.6
  • Escale factor=25, 𝑋=13.6, π‘Œ=48

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