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Worksheet: Applications of Similar Polygons

Q1:

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

  • Ayes , 0 . 8
  • Bno

Q2:

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

Q3:

Given that , find and the length of .

  • A ,
  • B ,
  • C ,
  • D ,

Q4:

Given that the rectangle 𝐴 𝐡 𝐢 𝐷 is similar to the rectangle 𝑋 𝐡 𝑍 π‘Œ , find the length of 𝑋 𝑍 .

Q5:

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

Q6:

If , , and , find .

  • A
  • B
  • C
  • D
  • E

Q7:

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

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

Q8:

Are the two polygons similar?

  • Ano
  • Byes

Q9:

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

Q10:

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

Q11:

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?

Q12:

Find π‘š ∠ 𝐢 + π‘š ∠ 𝐷 + π‘š ∠ 𝐸 .

Q13:

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

  • Aproportional
  • Bdifferent
  • Ccomplement
  • Dequal

Q14:

If , find .

  • A
  • B
  • C
  • D

Q15:

𝐴 𝐡 𝐢 𝐷 is mapped onto 𝐴 𝐡 𝐢 𝐷 β€² β€² β€² β€² by one or more of the following transformations: translation, reflection, rotation, dilation.

Determine the length of 𝐡 β€² 𝐢 β€² .

Determine the measure of angle 𝐢 𝐷 𝐴 .

Q16:

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

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