# 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.

**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 .

**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