Worksheet: Similar Polygons

In this worksheet, we will practice using proportions to find a missing side length in similar polygons.

Q1:

If 𝐴 𝐵 𝐶 𝐷 is similar to 𝑋 𝑌 𝑍 𝐿 , what is the length of 𝐴 𝐷 ?

Q2:

Given that triangles 𝐴 𝐵 𝐶 and 𝐴 𝐵 𝐶 are similar, work out the value of 𝑥 .

  • A 𝑥 = 2 . 5
  • B 𝑥 = 1 2
  • C 𝑥 = 6
  • D 𝑥 = 7
  • E 𝑥 = 5

Q3:

If 𝐵 𝐸 𝐹 𝐴 𝐸 𝐷 𝐶 𝐵 , find the value of 𝑥 .

Q4:

Given that 𝑄 𝑅 𝑃 𝑀 𝑆 𝑉 𝑍 𝑊 , find the value of 𝑥 .

Q5:

Given that the two polygons are similar, find the value of 𝑥 .

Q6:

These two shapes are similar, and their areas 𝐴 and 𝐴 are given. Find the value of 𝑥 .

Q7:

Given that the two given polygons are similar, determine the value of 𝑥 .

Q8:

Given that the two polygons are similar, find the value of 𝑥 .

Q9:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 8 , 𝑦 = 9
  • B 𝑥 = 1 6 , 𝑦 = 4
  • C 𝑥 = 8 , 𝑦 = 1 1
  • D 𝑥 = 1 6 , 𝑦 = 9
  • E 𝑥 = 1 0 , 𝑦 = 1 8

Q10:

Given that 𝐴 𝐵 𝐶 𝐷 𝑋 𝑌 𝑍 𝐿 , determine 𝑚 𝑋 𝑌 𝑍 .

Q11:

Given that 𝐴 𝐵 𝐶 𝐷 is similar to 𝑄 𝑆 𝑅 𝑃 , find the values of 𝑥 and 𝑦 .

  • A 𝑥 = 1 0 . 7 , 𝑦 = 4 6
  • B 𝑥 = 3 3 , 𝑦 = 4 9
  • C 𝑥 = 1 1 , 𝑦 = 4 6
  • D 𝑥 = 1 1 , 𝑦 = 4 9

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