Worksheet: Proportions in Similar Polygons

In this worksheet, we will practice using proportions in order to identify similar polygons.

Q1:

Are the two polygons similar?

  • Ano
  • Byes

Q2:

Given that the triangles shown are similar, determine 𝑥 .

  • A 7 2 5
  • B 4 5 8
  • C3
  • D 1 6 0 9

Q3:

Is the polygon 𝐴 𝐵 𝐶 𝐷 similar to the polygon 𝐸 𝐹 𝐺 𝐻 ?

  • Ayes
  • Bno

Q4:

Which of the following statements correctly defines similarity for polygons?

  • A Two polygons are said to be similar if their corresponding sides are equal.
  • B Two polygons are said to be similar if their corresponding angles are equal.
  • C Two polygons are said to be similar if their corresponding sides are congruent.
  • D Two polygons are said to be similar if their corresponding angles are congruent and their corresponding sides are in proportion.
  • ETwo polygons are said to be similar if their corresponding angles are complementary and their corresponding sides are equal.

Q5:

Find the lengths of 𝐴 𝐵 and 𝐴 𝐶 rounded to the nearest tenth.

  • A 1.8 cm, 1.3 cm
  • B 16.1 cm, 20.9 cm
  • C 40.3 cm, 50.8 cm
  • D 8.3 cm, 10.5 cm

Q6:

𝐴 𝐵 𝐶 𝐷 𝑍 𝑌 𝑋 𝐿 and the perimeter of 𝐴 𝐵 𝐶 𝐷 = 1 7 7 c m . Calculate the scale factor of similarity of 𝑍 𝑌 𝑋 𝐿 to 𝐴 𝐵 𝐶 𝐷 and the perimeter of 𝑍 𝑌 𝑋 𝐿 .

  • A scale factor = 1 4 , perimeter of 𝑍 𝑌 𝑋 𝐿 = 7 0 8 c m
  • B scale factor = 2 , perimeter of 𝑍 𝑌 𝑋 𝐿 = 3 5 4 c m
  • C scale factor = 1 4 , perimeter of 𝑍 𝑌 𝑋 𝐿 = 4 4 . 2 5 c m
  • D scale factor = 1 2 , perimeter of 𝑍 𝑌 𝑋 𝐿 = 8 8 . 5 c m
  • E scale factor = 1 2 , perimeter of 𝑍 𝑌 𝑋 𝐿 = 3 5 4 c m

Q7:

The ratio between corresponding sides of two similar triangles is 1 0 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.

Q8:

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.

Q9:

In the figure, given that the two triangles are similar, work out the value of 𝑥 .

  • A 𝑥 = 9 4
  • B 𝑥 = 7 2
  • C 𝑥 = 3 2
  • D 𝑥 = 2
  • E 𝑥 = 1 2

Q10:

Are the two polygons similar?

  • Ano
  • Byes

Q11:

If the corresponding angles in two triangles are equal, then the two triangles .

  • Aare not similar
  • Bare congruent
  • Chave the same area
  • Dare similar

Q12:

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

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

Q13:

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

  • A 3.5 cm, 5.5 cm, 4.5 cm, 9.5 cm, 5.5 cm
  • B 1.3 cm, 2.7 cm, 2 cm, 5.3 cm, 2.7 cm
  • C 4 cm, 5 cm, 4.5 cm, 13 cm, 5 cm
  • D 3 cm, 6 cm, 4.5 cm, 12 cm, 6 cm

Q14:

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

  • Adifferent
  • Bcongruent
  • Csimilar

Q15:

Consider two similar polygons 𝐴 𝐵 𝐶 𝐷 and 𝑋 𝑌 𝑍 𝐿 . Which angle in 𝐴 𝐵 𝐶 𝐷 corresponds to 𝑌 ?

  • A 𝐶
  • B 𝐴
  • C 𝐷
  • D 𝐵

Q16:

Is rectangle 𝐴 𝐵 𝐶 𝐷 similar to rectangle 𝑋 𝑌 𝑍 𝐿 ?

  • Ayes
  • Bno

Q17:

Any two triangles are similar when their corresponding are proportional.

  • Asides
  • Bangles

Q18:

If the polygon 𝑀 1 is similar to the polygon 𝑀 2 and the scale factor from 𝑀 1 to 𝑀 2 is positive and less than 1, then 𝑀 1 is 𝑀 2 .

  • Acongruent to
  • Ban enlargement of
  • Ca reduction of

Q19:

Consider the points 𝐴 ( 3 , 5 ) , 𝐵 ( 3 , 5 ) , 𝐶 ( 5 , 5 ) , 𝐷 ( 5 , 5 ) , 𝑊 ( 3 , 8 ) , 𝑋 ( 3 , 2 8 ) , 𝑌 ( 1 , 2 8 ) , and 𝑍 ( 1 , 8 ) . Is the rectangle 𝐴 𝐵 𝐶 𝐷 similar to the rectangle 𝑊 𝑋 𝑌 𝑍 ?

  • Ayes
  • Bno

Q20:

Are these two triangles similar?

  • Ayes
  • Bno

Q21:

Are these two polygons similar?

  • Ano
  • Byes

Q22:

Is polygon 𝐴 𝐵 𝐶 𝐷 similar to polygon 𝐺 𝐹 𝐸 𝑋 ?

  • Ayes
  • Bno

Q23:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 𝐺 𝐻 , determine the length of 𝐸 𝐻 .

Q24:

Find the length of 𝐶 𝐵 .

Q25:

A pair of corresponding sides in two similar polygons are of length 14 and 19. What is the ratio between their areas? What is the ratio between their perimeters?

  • A 1 9 6 3 6 1 , 5 6 1 9
  • B 4 2 1 9 , 1 9 6 3 6 1
  • C 1 4 1 9 , 5 6 1 9
  • D 1 9 6 3 6 1 , 1 4 1 9

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