# 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 .

• A
• B
• C3
• D

Q3:

Is the polygon similar to the polygon ?

• 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 and 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:

and the perimeter of . Calculate the scale factor of similarity of to and the perimeter of .

• A scale factor , perimeter of
• B scale factor , perimeter of
• C scale factor , perimeter of
• D scale factor, perimeter of
• E scale factor , perimeter of

Q7:

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

• A
• B
• C
• D
• E

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

• Bcongruent
• Csimilar

Q15:

Consider two similar polygons and . Which angle in corresponds to ?

• A
• B
• C
• D

Q16:

Is rectangle similar to rectangle ?

• Ayes
• Bno

Q17:

Any two triangles are similar when their corresponding are proportional.

• Asides
• Bangles

Q18:

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

• Acongruent to
• Ban enlargement of
• Ca reduction of

Q19:

Consider the points , , , , , , , and . Is the rectangle similar to the rectangle ?

• Ayes
• Bno

Q20:

Are these two triangles similar?

• Ayes
• Bno

Q21:

Are these two polygons similar?

• Ano
• Byes

Q22:

Is polygon similar to polygon ?

• Ayes
• Bno

Q23:

Given that , determine the length of .

Q24:

Find the length of .

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 ,
• B ,
• C ,
• D ,