Worksheet: Similar Polygons

In this worksheet, we will practice using 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 𝐴𝐵𝐶𝐷𝐸𝑃𝑄𝑅𝑆𝑇, find the scale factor of 𝐴𝐵𝐶𝐷𝐸 to 𝑃𝑄𝑅𝑆𝑇 and the perimeter of 𝑃𝑄𝑅𝑆𝑇.

  • AThe scale factor is 32, and the perimeter is 78.
  • BThe scale factor is 2714, and the perimeter is 117.
  • CThe scale factor is 23, and the perimeter is 64.
  • DThe scale factor is 1427, and the perimeter is 60.7.
  • EThe scale factor is 32, and the perimeter is 117 .

Q3:

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

  • Aproportional
  • Bdifferent
  • Ccomplement
  • Dequal

Q4:

If 𝐴𝐵𝐶𝑋𝑌𝑍, find the lengths of 𝐵𝐶 and 𝑋𝑍.

  • A𝐵𝐶=5cm, 𝑋𝑍=24cm
  • B𝐵𝐶=20cm, 𝑋𝑍=6cm
  • C𝐵𝐶=39.2cm, 𝑋𝑍=32.67cm

Q5:

Find 𝑚𝐶+𝑚𝐷+𝑚𝐸.

Q6:

Are these two polygons similar? If yes, find the scale factor from 𝑋𝑌𝑍𝐿 to 𝐴𝐵𝐶𝐷.

  • ANo
  • BYes,0.8

Q7:

Are the two polygons similar?

  • Ano
  • Byes

Q8:

If 𝐵𝐺𝐶𝐷𝐿𝑌𝑁𝑍, then 𝐵𝐺𝐶𝐷=𝑁𝑍.

  • A𝐵𝐺
  • B𝐿𝑌
  • C𝑌𝑁
  • D𝑍𝐿
  • E𝐺𝐶

Q9:

Given that 𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻, determine the length of 𝐺𝐻.

Q10:

Given that 𝐴𝐵𝐶𝐷𝑍𝑌𝑋𝐿, find 𝑚𝑋𝐿𝑍 and the length of 𝐶𝐷.

  • A𝑚𝑋𝐿𝑍=105, 𝐶𝐷=123.1cm
  • B𝑚𝑋𝐿𝑍=61, 𝐶𝐷=123.1cm
  • C𝑚𝑋𝐿𝑍=61, 𝐶𝐷=7.5cm
  • D𝑚𝑋𝐿𝑍=109, 𝐶𝐷=7.5cm

Q11:

If 𝑚𝐵+𝑚𝐶=145, find 𝑚𝑋.

Q12:

If 𝑋𝑌𝑍𝐴𝐵𝐶, 𝑚𝑌=26, and 𝑚𝐶=66, find 𝑚𝑋.

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 5312 inches wide. Find the height of the projected image.

  • A4912 in
  • B84114 in
  • C34122 in
  • D41922 in
  • E7914 in

Q14:

Given that the rectangle 𝐴𝐵𝐶𝐷 is similar to the rectangle 𝑋𝐵𝑍𝑌, find the length of 𝑋𝑍.

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.

  • Alength =15, area =150
  • Blength =12, area =96
  • Clength =8, area =96

Q16:

The image of a shape has a perimeter of 40 following a dilation by a scale factor of 12. What would the perimeter of the original shape be?

Q17:

A 1.97-meter-tall man stands 3.49 m away from a streetlight and casts a shadow that is 2.73 m long. How high is the lamp? Round your answer to the nearest tenth.

Q18:

𝐴𝐵𝐶𝐷 is mapped onto 𝐴𝐵𝐶𝐷 by one or more of the following transformations: translation, reflection, rotation, dilation.

Determine the length of 𝐵𝐶.

Determine the measure of angle 𝐶𝐷𝐴.

Q19:

Find the length of 𝐶𝐵.

Q20:

Consider the points 𝐴(3,5), 𝐵(3,5), 𝐶(5,5), 𝐷(5,5), 𝑊(3,8), 𝑋(3,28), 𝑌(1,28), and 𝑍(1,8). Is the rectangle 𝐴𝐵𝐶𝐷 similar to the rectangle 𝑊𝑋𝑌𝑍?

  • Ayes
  • Bno

Q21:

The ratio between corresponding sides of two similar triangles is 109. If the length of the base of the larger triangle is 19.7, find the length of the base of the smaller triangle rounding the answer to the nearest tenth.

Q22:

Which of the following statements correctly defines similarity for polygons?

  • ATwo polygons are said to be similar if their corresponding sides are equal.
  • BTwo polygons are said to be similar if their corresponding angles are complementary and their corresponding sides are equal.
  • CTwo polygons are said to be similar if their corresponding sides are congruent.
  • DTwo polygons are said to be similar if their corresponding angles are equal.
  • ETwo polygons are said to be similar if their corresponding angles are congruent and their corresponding sides are in proportion.

Q23:

The ratio between the areas of two similar polygons is 14. Given that the length of one side of the smaller one is 8 cm, calculate the length of the corresponding side of the bigger one.

Q24:

𝐴𝐵𝐶𝐷𝑍𝑌𝑋𝐿 and the perimeter of 𝐴𝐵𝐶𝐷=177cm. Calculate the scale factor of similarity of 𝑍𝑌𝑋𝐿 to 𝐴𝐵𝐶𝐷 and the perimeter of 𝑍𝑌𝑋𝐿.

  • Ascale factor=12, perimeter of 𝑍𝑌𝑋𝐿=88.5cm
  • Bscale factor =14, perimeter of 𝑍𝑌𝑋𝐿=708cm
  • Cscale factor =12, perimeter of 𝑍𝑌𝑋𝐿=354cm
  • Dscale factor =14, perimeter of 𝑍𝑌𝑋𝐿=44.25cm
  • Escale factor =2, perimeter of 𝑍𝑌𝑋𝐿=354cm

Q25:

Is the polygon 𝐴𝐵𝐶𝐷 similar to the polygon 𝐸𝐹𝐺𝐻?

  • Ano
  • Byes

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