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 π‘₯.

Q2:

If π΄π΅πΆπ·πΈβˆΌπ‘ƒπ‘„π‘…π‘†π‘‡, find the scale factor of 𝐴𝐡𝐢𝐷𝐸 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 β–³π΄π΅πΆβˆΌβ–³π‘‹π‘Œπ‘, find the lengths of 𝐡𝐢 and 𝑋𝑍.

  • 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‘šβˆ πΆ+π‘šβˆ π·+π‘šβˆ πΈ.

Q6:

Are these two polygons similar? If yes, find the scale factor from π‘‹π‘Œπ‘πΏ to 𝐴𝐡𝐢𝐷.

  • ANo
  • BYes,0.8

Q7:

Are the two polygons similar?

  • Ano
  • Byes

Q8:

If π΅πΊπΆπ·βˆΌπΏπ‘Œπ‘π‘, then 𝐡𝐺𝐢𝐷=…𝑁𝑍.

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

Q9:

Given that 𝐴𝐡𝐢𝐷∼𝐸𝐹𝐺𝐻, determine the length of 𝐺𝐻.

Q10:

Given that π΄π΅πΆπ·βˆΌπ‘π‘Œπ‘‹πΏ, find π‘šβˆ π‘‹πΏπ‘ and the length of 𝐢𝐷.

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

Q11:

If π‘šβˆ π΅+π‘šβˆ πΆ=145∘, find π‘šβˆ π‘‹.

Q12:

If β–³π‘‹π‘Œπ‘βˆΌβ–³π΄π΅πΆ, π‘šβˆ π‘Œ=26∘, and π‘šβˆ πΆ=66∘, find π‘šβˆ π‘‹.

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.

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

Q14:

Given that the rectangle 𝐴𝐡𝐢𝐷 is similar to the rectangle π‘‹π΅π‘π‘Œ, 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:

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

Determine the length of 𝐡′𝐢′.

Determine the measure of angle 𝐢𝐷𝐴.

Q19:

Find the length of 𝐢𝐡.

Q20:

Consider the points 𝐴(3,5), 𝐡(3,βˆ’5), 𝐢(5,βˆ’5), 𝐷(5,5), π‘Š(βˆ’3,8), 𝑋(βˆ’3,28), π‘Œ(1,28), and 𝑍(1,8). Is the rectangle 𝐴𝐡𝐢𝐷 similar to the rectangle π‘Šπ‘‹π‘Œπ‘?

  • Ayes
  • Bno

Q21:

The ratio between corresponding sides of two similar triangles is 10∢9. 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 1∢4. 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:

𝐴 𝐡 𝐢 𝐷 ∼ 𝑍 π‘Œ 𝑋 𝐿 and the perimeter of 𝐴𝐡𝐢𝐷=177cm. Calculate the scale factor of similarity of π‘π‘Œπ‘‹πΏ to 𝐴𝐡𝐢𝐷 and the perimeter of π‘π‘Œπ‘‹πΏ.

  • Ascale factor=12, perimeter of π‘π‘Œπ‘‹πΏ=88.5cm
  • Bscale factor =14, perimeter of π‘π‘Œπ‘‹πΏ=708cm
  • Cscale factor =12, perimeter of π‘π‘Œπ‘‹πΏ=354cm
  • Dscale factor =14, perimeter of π‘π‘Œπ‘‹πΏ=44.25cm
  • Escale factor =2, perimeter of π‘π‘Œπ‘‹πΏ=354cm

Q25:

Is the polygon 𝐴𝐡𝐢𝐷 similar to the polygon 𝐸𝐹𝐺𝐻?

  • Ano
  • Byes

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