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?