# 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.

**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

**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 .

- Adifferent
- 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 .

**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?