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:

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.

Q2:

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

Q3:

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

Q4:

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

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

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:

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

Q7:

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

Q8:

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

Q9:

Is polygon 𝐴𝐡𝐢𝐷 similar to polygon 𝐺𝐹𝐸𝑋?

  • ANo
  • BYes

Q10:

A college professor was using a projector to give his lectures. A slide whose dimensions are 11 centimeters wide and 7 centimeters high was projected into an image that was 5312 centimeters wide. Find the height of the projected image.

  • A4912 cm
  • B84114 cm
  • C34122 cm
  • D41922 cm
  • E7914 cm

Practice Means Progress

Download the Nagwa Practice app to access 32 additional questions for this lesson!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.