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
