# 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 . Q2:

If , find the scale factor of to and the perimeter of . • AThe scale factor is , and the perimeter is 78.
• BThe scale factor is , and the perimeter is 117.
• CThe scale factor is , and the perimeter is 64.
• DThe scale factor is , and the perimeter is 60.7.
• EThe scale factor is , and the perimeter is 117 .

Q3:

If , then .

• A
• B
• C
• D
• E

Q4:

Given that , determine the length of . Q5:

Given that , find and the length of . • A,
• B,
• C,
• D,

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 inches wide. Find the height of the projected image.

• A in
• B in
• C in
• D in
• E in

Q7:

Given that the rectangle is similar to the rectangle , find the length of . 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 , area
• Blength , area
• Clength , area

Q9:

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

• 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 . 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:

and the perimeter of . Calculate the scale factor of similarity of to and the perimeter of . • Ascale factor, perimeter of
• Bscale factor , perimeter of
• Cscale factor , perimeter of
• Dscale factor , perimeter of
• Escale factor , perimeter of

Q13:

Given that , determine the length of . 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 and polygon are both similar to a third polygon, then polygons and are .

• Bsimilar
• Ccongruent

Q18:

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

• A
• B
• C
• D

Q19:

Given that is similar to , and the perimeter of is 66.2, calculate the perimeter of . Q20:

Given that the rectangles shown are similar, what is ? Q21:

A square and a rectangle are .

• Asimilar
• Bcongruent
• Cnot similar
• Dproportional

Q22:

Given that the similarity ratio of polygon to polygon and the similarity ratio of polygon to polygon , find the similarity ratio of polygon to polygon .

• A
• B
• C
• D

Q23:

In the figure below, . If and , find the length of . Q24:

Quadrilaterals and 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?