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Lesson: Applications of Similar Polygons

Sample Question Videos

Worksheet • 16 Questions • 3 Videos

Q1:

If the two following polygons are similar, find the value of π‘₯ .

Q2:

If 𝐴 𝐡 𝐢 𝐷 𝐸 ∼ 𝑃 𝑄 𝑅 𝑆 𝑇 , find the scale factor of 𝐴 𝐡 𝐢 𝐷 𝐸 to 𝑃 𝑄 𝑅 𝑆 𝑇 and the perimeter of 𝑃 𝑄 𝑅 𝑆 𝑇 .

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

Q3:

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

  • Aequal
  • Bdifferent
  • Ccomplement
  • Dproportional

Q4:

If β–³ 𝐴 𝐡 𝐢 ∼ β–³ 𝑋 π‘Œ 𝑍 , find the lengths of 𝐡 𝐢 and 𝑋 𝑍 .

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

Q5:

Find π‘š ∠ 𝐢 + π‘š ∠ 𝐷 + π‘š ∠ 𝐸 .

Q6:

Are these two polygons similar? If yes, find the scale factor from 𝑋 π‘Œ 𝑍 𝐿 to 𝐴 𝐡 𝐢 𝐷 .

  • Ano
  • Byes , 0 . 8

Q7:

Are the two polygons similar?

  • Ayes
  • Bno

Q8:

If 𝐡 𝐺 𝐢 𝐷 ∼ 𝐿 π‘Œ 𝑁 𝑍 , then 𝐡 𝐺 𝐢 𝐷 = … 𝑁 𝑍 .

  • A 𝐿 π‘Œ
  • B 𝐺 𝐢
  • C π‘Œ 𝑁
  • D 𝐡 𝐺
  • E 𝑍 𝐿

Q9:

Given that 𝐴 𝐡 𝐢 𝐷 ∼ 𝐸 𝐹 𝐺 𝐻 , determine the length of 𝐺 𝐻 .

Q10:

Given that 𝐴 𝐡 𝐢 𝐷 ∼ 𝑍 π‘Œ 𝑋 𝐿 , find π‘š ∠ 𝑋 𝐿 𝑍 and the length of 𝐢 𝐷 .

  • A π‘š ∠ 𝑋 𝐿 𝑍 = 6 1 ∘ , 𝐢 𝐷 = 1 2 3 . 1 c m
  • B π‘š ∠ 𝑋 𝐿 𝑍 = 1 0 9 ∘ , 𝐢 𝐷 = 7 5 c m
  • C π‘š ∠ 𝑋 𝐿 𝑍 = 6 1 ∘ , 𝐢 𝐷 = 7 5 c m
  • D π‘š ∠ 𝑋 𝐿 𝑍 = 1 0 5 ∘ , 𝐢 𝐷 = 1 2 3 . 1 c m

Q11:

If π‘š ∠ 𝐡 + π‘š ∠ 𝐢 = 1 4 5 ∘ , find π‘š ∠ 𝑋 .

Q12:

If β–³ 𝑋 π‘Œ 𝑍 ∼ β–³ 𝐴 𝐡 𝐢 , π‘š ∠ π‘Œ = 2 6 ∘ , and π‘š ∠ 𝐢 = 6 6 ∘ , find π‘š ∠ 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 3 4 1 2 2 in
  • B 7 9 1 4 in
  • C 8 4 1 1 4 in
  • D 4 1 9 2 2 in
  • E 4 9 1 2 in

Q14:

Given that the rectangle 𝐴 𝐡 𝐢 𝐷 is similar to the rectangle 𝑋 𝐡 𝑍 π‘Œ , 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 = 8 , area = 9 6
  • B length = 1 2 , area = 9 6
  • C length = 1 5 , area = 1 5 0

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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