Worksheet: Applications of Similar Polygons

In this worksheet, we will practice using the properties of similar polygons to solve algebraic expressions and equations.

Q1:

If 𝐴𝐵𝐶𝐷 is similar to 𝑋𝑌𝑍𝐿, what is the length of 𝐴𝐷?

Q2:

Given that triangles 𝐴𝐵𝐶 and 𝐴𝐵𝐶 are similar, work out the value of 𝑥.

  • A𝑥=12
  • B𝑥=7
  • C𝑥=5
  • D𝑥=2.5
  • E𝑥=6

Q3:

If 𝐵𝐸𝐹𝐴𝐸𝐷𝐶𝐵, find the value of 𝑥.

Q4:

Given that 𝑄𝑅𝑃𝑀𝑆𝑉𝑍𝑊, 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.

  • A3
  • B2
  • C2.5
  • D5

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 𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻, find the values of 𝑥 and 𝑦.

  • A𝑥=16, 𝑦=9
  • B𝑥=16, 𝑦=4
  • C𝑥=10, 𝑦=18
  • D𝑥=8, 𝑦=11
  • E𝑥=8, 𝑦=9

Q10:

Given that 𝐴𝐵𝐶𝐷𝑋𝑌𝑍𝐿, determine 𝑚𝑋𝑌𝑍.

Q11:

Given that 𝐴𝐵𝐶𝐷 is similar to 𝑄𝑆𝑅𝑃, find the values of 𝑥 and 𝑦.

  • A𝑥=11, 𝑦=49
  • B𝑥=10.7, 𝑦=46
  • C𝑥=33, 𝑦=49
  • D𝑥=11, 𝑦=46

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