# Worksheet: Similar Polygons

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 two triangles are similar, then their corresponding angles are .

• Aproportional
• Bdifferent
• Ccomplement
• Dequal

Q4:

If , find the lengths of and . • A,
• B,
• C,

Q5:

Find . Q6:

Are these two polygons similar? If yes, find the scale factor from to . • ANo
• BYes

Q7:

Are the two polygons similar? • Ano
• Byes

Q8:

If , then .

• A
• B
• C
• D
• E

Q9:

Given that , determine the length of . Q10:

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

Q11:

If , find . Q12:

If , , and , find .

Q13:

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

Q14:

Given that the rectangle is similar to the rectangle , find the length of . Q15:

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

Q16:

The image of a shape has a perimeter of 40 following a dilation by a scale factor of . What would the perimeter of the original shape be?

Q17:

A 1.97-meter-tall man stands 3.49 m away from a streetlight and casts a shadow that is 2.73 m long. How high is the lamp? Round your answer to the nearest tenth.

Q18:

is mapped onto by one or more of the following transformations: translation, reflection, rotation, dilation. Determine the length of .

Determine the measure of angle .

Q19:

Find the length of . Q20:

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

• Ayes
• Bno

Q21:

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.

Q22:

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.

Q23:

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.

Q24:

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

Q25:

Is the polygon similar to the polygon ? • Ano
• Byes