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Worksheet: Similar Triangles

Q1:

Given that 𝐷 𝐸 = 7 4 m , 𝐸 𝐡 = 3 2 m , and 𝐸 𝐴 = 4 8 m , find the length of 𝐢 𝐴 .

Q2:

Find the value of π‘₯ .

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

Q3:

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

Q4:

If β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝐴 𝐷 𝐸 , evaluate π‘₯ .

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

Q5:

In the given figure, 𝐷 𝐸 and 𝐡 𝐢 are parallel. Use similarity to work out the value of π‘₯ .

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

Q6:

𝐴 𝐡 𝐢 𝐷 𝐸 ∼ 𝐹 𝐺 𝐻 𝐾 𝑀 where 𝐴 𝐢 = 4 6 c m and 𝐹 𝐻 = 1 1 . 5 c m . If the area of 𝐴 𝐡 𝐢 𝐷 𝐸 = 3 0 3 6 c m 2 , what is the area of 𝐹 𝐺 𝐻 𝐾 𝑀 ?

Q7:

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?

Q8:

Given that 𝐴 𝐷 𝐷 𝐢 = 3 7 and the area of β–³ 𝐴 𝐡 𝐢 = 4 8 4 c m 2 , find the area of β–³ 𝐴 𝐷 𝐸 .

Q9:

𝐴 𝐡 𝐢 𝐷 ∼ 𝐸 𝐹 𝐺 𝐻 where 𝐴 𝑁 = 7 c m and 𝐸 𝑀 = 2 . 8 c m . If the area of 𝐴 𝐡 𝐢 𝐷 is 1 848 cm2, what is the area of 𝐸 𝐹 𝐺 𝐻 ?

Q10:

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

Q11:

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.

Q12:

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.

Q13:

If 𝐴 𝐡 𝐢 𝐷 ∼ 𝐸 𝐹 𝐺 𝐻 , find the scale factor of similarity of 𝐸 𝐹 𝐺 𝐻 to 𝐴 𝐡 𝐢 𝐷 and the values of 𝑋 and π‘Œ .

  • A scale factor = 2 5 , 𝑋 = 1 3 . 6 , π‘Œ = 4 8
  • B scale factor = 2 5 , 𝑋 = 4 4 , π‘Œ = 1 3 . 6
  • C scale factor = 1 2 , 𝑋 = 8 5 , π‘Œ = 3 . 6 8
  • D scale factor = 2 5 , 𝑋 = 1 3 . 6 , π‘Œ = 4 4
  • E scale factor = 4 2 5 , 𝑋 = 5 . 4 4 , π‘Œ = 1 1 6

Q14:

Given that the similarity ratio of polygon 𝐴 𝐡 𝐢 𝐷 to polygon 𝐸 𝐹 𝐺 𝐻 = 5 4 and the similarity ratio of polygon 𝑋 π‘Œ 𝑍 𝐿 to polygon 𝐸 𝐹 𝐺 𝐻 = 7 6 , find the similarity ratio of polygon 𝐴 𝐡 𝐢 𝐷 to polygon 𝑋 π‘Œ 𝑍 𝐿 .

  • A 4 5
  • B 3 5 2 4
  • C 1 4 1 5
  • D 1 5 1 4

Q15:

Given that 𝐸 𝐷 = 1 0 c m , 𝐴 𝐸 = 8 c m , 𝐸 𝐢 = 2 0 c m , and 𝐡 𝐷 = 1 5 c m , find the length of 𝐡 𝐢 .

Q16:

Triangles 𝐴 𝐡 𝐢 and 𝐴 𝐡 𝐢 β€² β€² β€² are similar.

Work out the value of π‘₯ .

Work out the value of 𝑦 .

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

Q17:

In the figure, suppose also that 𝐹 𝑁 = 𝐷 𝑁 = 2 , and that 𝐡 𝐹 = 1 . What is the length 𝐢 𝐸 ?

Q18:

In triangle , let be a point on and a point on . Suppose that and that . If the area of is 237, what is the area of the trapezoid ?

  • A131.67
  • B94.8
  • C85.32
  • D151.68
  • E211.34

Q19:

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

Q20:

The areas of two similar polygons are in the ratio 8 1 1 2 1 . What is the ratio between corresponding sides? What is the ratio between their perimeters?

  • A 8 1 1 2 1 , 9 1 1
  • B 9 1 1 , 4 5 1 1
  • C 8 1 1 2 1 , 4 5 1 1
  • D 9 1 1 , 9 1 1

Q21:

If β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝐷 𝐸 𝐹 , the area of 𝐴 𝐡 𝐢 = 9 1 6 9 of the area of 𝐷 𝐸 𝐹 , and 𝐷 𝐸 = 6 c m , find the length of 𝐴 𝐡 .

  • A 1 2 6 cm
  • B 26 cm
  • C 6 cm
  • D 1 8 1 3 cm

Q22:

Triangles 𝐴 𝐡 𝐢 and 𝐴 𝐷 𝐸 are similar. Find π‘₯ to the nearest integer.

Q23:

Triangle 𝐴 𝐡 𝐢 can be dilated by a scale factor of two onto triangle 𝐴 𝐡 𝐢 β€² β€² β€² .

Determine the length of 𝐴 β€² 𝐡 β€² .

Determine the length of 𝐴 β€² 𝐢 β€² .

Find the measure of angle 𝐴 β€² 𝐡 β€² 𝐢 β€² .

Q24:

Given that is a square, , and , find .

  • A
  • B110
  • C15
  • D10

Q25:

Triangles 𝐴 𝐡 𝐢 and 𝐴 𝐡 𝐢 β€² β€² β€² are similar.

Work out the measure of angle π‘₯ .

Work out the value of 𝑦 .

Work out the value of 𝑧 .