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.

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

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

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

Q10:

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.

Q11:

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.

Q12:

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

Q13:

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

Q14:

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.

Q15:

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

Q16:

Are all golden rectangles similar?

  • AYes
  • BNo

Q17:

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

  • Adifferent
  • Bsimilar
  • Ccongruent

Q18:

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

Q19:

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.

Q20:

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

Q21:

A square and a rectangle are .

  • Asimilar
  • Bcongruent
  • Cnot similar
  • Dproportional

Q22:

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

Q23:

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

Q24:

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

Q25:

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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