Lesson Worksheet: Similar Polygons Mathematics • 8th Grade

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


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


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 .


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

  • A𝐡𝐺
  • BπΏπ‘Œ
  • Cπ‘Œπ‘
  • D𝑍𝐿
  • E𝐺𝐢


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


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

  • Aπ‘šβˆ π‘‹πΏπ‘=105∘, 𝐢𝐷=123.1cm
  • Bπ‘šβˆ π‘‹πΏπ‘=61∘, 𝐢𝐷=123.1cm
  • Cπ‘šβˆ π‘‹πΏπ‘=61∘, 𝐢𝐷=7.5cm
  • Dπ‘šβˆ π‘‹πΏπ‘=109∘, 𝐢𝐷=7.5cm


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


Given that the rectangle 𝐴𝐡𝐢𝐷 is similar to the rectangle π‘‹π΅π‘π‘Œ, find the length of 𝑋𝑍.


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


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


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.


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.


π΄π΅πΆπ·βˆΌπ‘π‘Œπ‘‹πΏ 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


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


If the scale factor of two similar polygons equals 1, what can you say about the polygons?

  • AThey are congruent.
  • BThey are different.
  • CThey are just similar.


A polygon has sides 2, 4, 3, 8, and 4. A second similar polygon has perimeter 31.5. What are its sides?

  • A1.3 cm, 2.7 cm, 2 cm, 5.3 cm, 2.7 cm
  • B3.5 cm, 5.5 cm, 4.5 cm, 9.5 cm, 5.5 cm
  • C4 cm, 5 cm, 4.5 cm, 13 cm, 5 cm
  • D3 cm, 6 cm, 4.5 cm, 12 cm, 6 cm


Are all golden rectangles similar?

  • AYes
  • BNo


If polygon 𝐴 and polygon 𝐡 are both similar to a third polygon, then polygons 𝐴 and 𝐡 are .

  • Adifferent
  • Bsimilar
  • Ccongruent


Consider two similar polygons 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ. Which angle in 𝐴𝐡𝐢𝐷 corresponds to βˆ π‘Œ?

  • A∠𝐢
  • B∠𝐡
  • C∠𝐷
  • D∠𝐴


Given that 𝐴𝐡𝐢𝐷 is similar to π‘‹π‘Œπ‘πΏ, and the perimeter of 𝐴𝐡𝐢𝐷 is 66.2, calculate the perimeter of π‘‹π‘Œπ‘πΏ.


Given that the rectangles shown are similar, what is π‘₯?


A square and a rectangle are .

  • Asimilar
  • Bcongruent
  • Cnot similar
  • Dproportional


Given that the similarity ratio of polygon 𝐴𝐡𝐢𝐷 to polygon 𝐸𝐹𝐺𝐻=54 and the similarity ratio of polygon π‘‹π‘Œπ‘πΏ to polygon 𝐸𝐹𝐺𝐻=76, find the similarity ratio of polygon 𝐴𝐡𝐢𝐷 to polygon π‘‹π‘Œπ‘πΏ.

  • A3524
  • B45
  • C1514
  • D1415


In the figure below, π΄π΅πΆπ·βˆΌπ‘‹πΈπΆπΉ. If 𝑋𝐸=12𝐴𝐡 and 𝐢𝐹=20cm, find the length of 𝐹𝐷.


Quadrilaterals 𝐴𝐡𝐢𝐷 and π‘‹π‘Œπ‘πΏ are similar. Determine the ratio of enlargement rounded to two decimal places if necessary.


A rectangle is similar to one with sides 13 and 10. If the scale factor from the first to the second is 0.9, what is the area of the first rectangle?

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