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 𝐷 𝐸 = 7 4 m , 𝐸 𝐵 = 3 2 m , and 𝐸 𝐴 = 4 8 m , find the length of 𝐶 𝐴 .

Q3:

In the given figure, 𝐷 𝐸 and 𝐵 𝐶 are parallel. Use similarity to work out the value of 𝑥 .

  • A 𝑥 = 5
  • B 𝑥 = 6
  • C 𝑥 = 6 8
  • D 𝑥 = 3
  • E 𝑥 = 1

Q4:

If 𝐴 𝐵 𝐶 𝐴 𝐷 𝐸 , evaluate 𝑥 .

  • A 3 1 1 3
  • B97
  • C 7 3 1 1
  • D 7 1 7

Q5:

Given that 𝐹 𝐺 𝐻 𝑋 𝑌 𝑍 , if 6 units are added to the length of each side, are the new triangles similar?

  • Ano
  • Byes

Q6:

Find the value of 𝑥 .

  • A2
  • B 2 5 4
  • C 7 2
  • D 1 9 4

Q7:

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

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

Q8:

Fill in the blank: 𝐴 𝐵 𝐶 .

  • A 𝐶 𝐴 𝐷 , 𝐴 𝐵 𝐷
  • B 𝐴 𝐷 𝐶 , 𝐴 𝐷 𝐵
  • C 𝐷 𝐶 𝐴 , 𝐷 𝐴 𝐵
  • D 𝐷 𝐴 𝐶 , 𝐷 𝐵 𝐴

Q9:

Given that 𝐴 𝐵 𝐶 and 𝐷 𝐸 𝐹 are similar, find the length of 𝐷 𝐻 .

Q10:

𝑋 𝑌 𝑍 is a right-angled triangle at 𝑋 . 𝐿 is a point on 𝑌 𝑍 such that 𝑋 𝐿 𝑌 𝑍 . If 𝑋 𝑍 = 1 9 c m and 𝑋 𝑌 = 8 c m , calculate the lengths of 𝑌 𝐿 and 𝑋 𝐿 . Round your answers to the nearest hundredth.

  • A 𝑌 𝐿 = 1 7 . 5 1 c m , 𝑋 𝐿 = 7 . 3 7 c m
  • B 𝑌 𝐿 = 1 7 . 5 1 c m , 𝑋 𝐿 = 3 . 1 0 c m
  • C 𝑌 𝐿 = 3 . 1 0 c m , 𝑋 𝐿 = 2 . 9 5 c m
  • D 𝑌 𝐿 = 3 . 1 0 c m , 𝑋 𝐿 = 7 . 3 7 c m

Q11:

Triangles 𝐴 𝐵 𝐶 and 𝐴 𝐵 𝐶 are similar.

Work out the value of 𝑥 .

Work out the value of 𝑦 .

  • A 2 1 5
  • B 5 0 3
  • C7
  • D6
  • E 3 5 3

Q12:

Triangles 𝐴 𝐵 𝐶 and 𝐴 𝐵 𝐶 are similar.

Work out the length of 𝐴 𝐶 .

Work out the length of 𝐵 𝐶 .

Q13:

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

Determine the length of .

  • A3
  • B6
  • C8
  • D4

Determine the length of .

  • A9
  • B3
  • C4
  • D6

Find the size of angle .

  • A
  • B
  • C

Q14:

Triangles and are similar.

Work out the size of angle .

  • A
  • B
  • C
  • D
  • E

Work out the value of .

  • A 7.5
  • B6.4
  • C8
  • D6
  • E3

Work out the value of .

  • A1.5
  • B4
  • C1.6
  • D3.6
  • E2.5

Q15:

Given that 𝑋 𝑌 𝑍 𝐿 is a square, 𝑚 𝑌 𝑀 𝑍 = ( 𝑘 + 8 4 ) , and 𝑚 𝑀 𝑌 𝑍 = ( 𝑘 + 3 3 ) , find 𝑘 .

Q16:

Find the value of rounded to the nearest hundredth, if needed.

Q17:

Triangles 𝐴 𝐵 𝐶 and 𝐴 𝐷 𝐸 are similar. Find 𝑥 to the nearest integer.

Q18:

Given that 𝐴 𝐷 𝐷 𝐶 = 3 7 and the area of 𝐴 𝐵 𝐶 = 4 8 4 c m , find the area of 𝐴 𝐷 𝐸 .

Q19:

𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 𝐾 𝑀 where 𝐴 𝐶 = 4 6 c m and 𝐹 𝐻 = 1 1 . 5 c m . If the area of 𝐴 𝐵 𝐶 𝐷 𝐸 = 3 , 0 3 6 c m , what is the area of 𝐹 𝐺 𝐻 𝐾 𝑀 ?

Q20:

The diagonal of a small square is 3 4 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 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 where 𝐴 𝑁 = 7 c m and 𝐸 𝑀 = 2 . 8 c m . If the area of 𝐴 𝐵 𝐶 𝐷 is 1,848 cm2, what is the area of 𝐸 𝐹 𝐺 𝐻 ?

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 7 6
  • C 1 4 3
  • D 4 9 3 6
  • E 7 2

Q23:

Square A is an enlargement of Square B by a scale factor of 2 3 . 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 , 7 9 9 p o u n d s 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 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 , find the scale factor of similarity of 𝐸 𝐹 𝐺 𝐻 to 𝐴 𝐵 𝐶 𝐷 and the values of 𝑋 and 𝑌 .

  • A scale factor = 2 5 , 𝑋 = 1 3 . 6 , 𝑌 = 4 8
  • B scale factor = 2 5 , 𝑋 = 4 4 , 𝑌 = 1 3 . 6
  • C scale factor = 1 2 , 𝑋 = 8 5 , 𝑌 = 3 . 6 8
  • D scale factor = 2 5 , 𝑋 = 1 3 . 6 , 𝑌 = 4 4
  • E scale factor = 4 2 5 , 𝑋 = 5 . 4 4 , 𝑌 = 1 1 6

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