In this worksheet, we will practice using proportions in order to identify similar polygons.

**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 .

- Adifferent
- 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 ,