Worksheet: Applications of Similar Polygons

In this worksheet, we will practice how to use the properties of similar polygons to find unknown angles, side lengths, scale factors, and perimeters.

Q1:

If the two following polygons are similar, find the value of 𝑥 .

Q2:

If 𝐴 𝐵 𝐶 𝐷 𝐸 𝑃 𝑄 𝑅 𝑆 𝑇 , find the scale factor of 𝐴 𝐵 𝐶 𝐷 𝐸 to 𝑃 𝑄 𝑅 𝑆 𝑇 and the perimeter of 𝑃 𝑄 𝑅 𝑆 𝑇 .

  • AThe scale factor is 2 7 1 4 , and the perimeter is 117.
  • BThe scale factor is 2 3 , and the perimeter is 64.
  • CThe scale factor is 1 4 2 7 , and the perimeter is 60.7.
  • DThe scale factor is 3 2 , and the perimeter is 78.
  • EThe scale factor is 3 2 , and the perimeter is 117.

Q3:

If two triangles are similar, then their corresponding angles are .

  • Aproportional
  • Bdifferent
  • Ccomplement
  • Dequal

Q4:

If 𝐴 𝐵 𝐶 𝑋 𝑌 𝑍 , find the lengths of 𝐵 𝐶 and 𝑋 𝑍 .

  • A 𝐵 𝐶 = 3 9 . 2 c m , 𝑋 𝑍 = 3 2 . 6 7 c m
  • B 𝐵 𝐶 = 5 c m , 𝑋 𝑍 = 2 4 c m
  • C 𝐵 𝐶 = 2 0 c m , 𝑋 𝑍 = 6 c m

Q5:

Find 𝑚 𝐶 + 𝑚 𝐷 + 𝑚 𝐸 .

Q6:

Are these two polygons similar? If yes, find the scale factor from 𝑋 𝑌 𝑍 𝐿 to 𝐴 𝐵 𝐶 𝐷 .

  • Ayes , 0 . 8
  • Bno

Q7:

Are the two polygons similar?

  • Ano
  • Byes

Q8:

If 𝐵 𝐺 𝐶 𝐷 𝐿 𝑌 𝑁 𝑍 , then 𝐵 𝐺 𝐶 𝐷 = 𝑁 𝑍 .

  • A 𝑍 𝐿
  • B 𝑌 𝑁
  • C 𝐵 𝐺
  • D 𝐿 𝑌
  • E 𝐺 𝐶

Q9:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 , determine the length of 𝐺 𝐻 .

Q10:

Given that 𝐴 𝐵 𝐶 𝐷 𝑍 𝑌 𝑋 𝐿 , find 𝑚 𝑋 𝐿 𝑍 and the length of 𝐶 𝐷 .

  • A 𝑚 𝑋 𝐿 𝑍 = 1 0 5 , 𝐶 𝐷 = 1 2 3 . 1 c m
  • B 𝑚 𝑋 𝐿 𝑍 = 1 0 9 , 𝐶 𝐷 = 7 5 c m
  • C 𝑚 𝑋 𝐿 𝑍 = 6 1 , 𝐶 𝐷 = 7 5 c m
  • D 𝑚 𝑋 𝐿 𝑍 = 6 1 , 𝐶 𝐷 = 1 2 3 . 1 c m

Q11:

If 𝑚 𝐵 + 𝑚 𝐶 = 1 4 5 , find 𝑚 𝑋 .

Q12:

If 𝑋 𝑌 𝑍 𝐴 𝐵 𝐶 , 𝑚 𝑌 = 2 6 , and 𝑚 𝐶 = 6 6 , find 𝑚 𝑋 .

Q13:

A college professor was using a projector to give his lectures. A slide whose dimensions are 11 inches wide and 7 inches high was projected into an image that was 5 3 1 2 inches wide. Find the height of the projected image.

  • A 4 9 1 2 in
  • B 8 4 1 1 4 in
  • C 4 1 9 2 2 in
  • D 3 4 1 2 2 in
  • E 7 9 1 4 in

Q14:

Given that the rectangle 𝐴 𝐵 𝐶 𝐷 is similar to the rectangle 𝑋 𝐵 𝑍 𝑌 , find the length of 𝑋 𝑍 .

Q15:

A rectangle that is 15 by 10 is similar to a second rectangle with perimeter 40. Find the length and the area of the second rectangle.

  • A length = 1 5 , area = 1 5 0
  • B length = 8 , area = 9 6
  • C length = 1 2 , area = 9 6

Q16:

The image of a shape has a perimeter of 40 following a dilation by a scale factor of 1 2 . What would the perimeter of the original shape be?

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