Geometry and proof · Ages 14–15

Similar polygons worksheet

Part of: Similar triangles

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Geometry and proof · Ages 14–15

Numsprite
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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.ABCD ~ PQRS, with ∠A = 115°, ∠B = 75° and ∠C = 120°. ∠S =
Answer:
2.In the picture, ABCD ~ PQRS. x =
Answer:
3.ABCD ~ PQRS, with ∠A = 115°, ∠B = 100° and ∠C = 75°. ∠S =
Answer:
4.In the picture, ABCD ~ PQRS. x =
Answer:
5.A photo 13 cm long and 4 cm wide is enlarged into a similar one 8 cm wide. Its length =
Answer:
6.In the picture, KLMN ~ PQRS. x = , y =
Fill in each blank
Answer:
7.A photo 14 cm long and 7 cm wide is enlarged into a similar one 12 cm wide. Its length =
Answer:
8.A photo 12 cm long and 4 cm wide is enlarged into a similar one 7 cm wide. Its length =
Answer:

9.A rectangle 10 cm long and 2 cm wide is similar to one 15 cm long and 4 cm wide.
True or false?
Answer:
10.A rectangle 6 cm long and 4 cm wide is similar to one 12 cm long and 9 cm wide.
True or false?
Answer:
11.A rectangle 12 cm long and 4 cm wide is similar to one 6 cm long and 2 cm wide.
True or false?
Answer:
12.Which pair of figures must be similar?
- A. two squares
- B. two isosceles triangles
- C. two rhombuses
- D. two rectangles
Choose the right answer
Answer:

13.Two TVs have rectangular screens of the same shape. The small screen is 15 cm long and 10 cm wide; the big one is 72 cm wide. How long is the big screen?
Working:
Answer:
14.A photo 15 cm long and 6 cm wide is enlarged to 37.5 cm long, similar to the original. Scale = , and the enlarged width = cm.
Fill in each blank
Working:
Answer:
15.A picture frame's outer edge is a rectangle 19 cm by 19 cm, and the frame is 2 cm wide all round. The rectangle inside the frame is similar to the outer one.
True or false?
Working:
Answer:
16.A model of a four-sided garden has sides of 9 cm, 8 cm, 3 cm and 7 cm; the real garden is similar, at 1 : 200. The model's perimeter = cm, and the real garden's = m.
Fill in each blank
Working:
Answer:
17.A picture frame's outer edge is a rectangle 17 cm by 28 cm, and the frame is 3 cm wide all round. The rectangle inside the frame is similar to the outer one.
True or false?
Working:
Answer:
18.A model of a four-sided garden has sides of 7 cm, 9 cm, 4 cm and 9 cm; the real garden is similar, at 1 : 200. The model's perimeter = cm, and the real garden's = m.
Fill in each blank
Working:
Answer:

Show the answers and working

Similar polygons worksheet: Answers and working

1. 50°
∠S goes with ∠D = 360° − 115° − 75° − 120° = 50° (∠ sum of polygon); similar figures keep their angles.
2. 4.5 cm
Scale = PQ ÷ AB = 9 ÷ 6 = 1.5; QR goes with BC: x = 3 × 1.5 = 4.5.
3. 70°
∠S goes with ∠D = 360° − 115° − 100° − 75° = 70° (∠ sum of polygon); similar figures keep their angles.
4. 80°
x is ∠S, which goes with ∠D = 360° − 105° − 100° − 75° = 80°: similar figures' angles are equal, never scaled.
5. 26 cm
Width with width, length with length: the scale is 8 ÷ 4, so the length = 13 × 8 ÷ 4 = 26 cm.
6. 8, 105
Scale = 12 ÷ 6 = 2: x = 4 × 2 = 8; y is ∠Q, equal to ∠L = 105° — angles aren't scaled.
7. 24 cm
Width with width, length with length: the scale is 12 ÷ 7, so the length = 14 × 12 ÷ 7 = 24 cm.
8. 21 cm
Width with width, length with length: the scale is 7 ÷ 4, so the length = 12 × 7 ÷ 4 = 21 cm.

9. False
Rectangles' angles are all 90°, so look at the sides: similar only if 1510 and 42 are equal.
10. False
Rectangles' angles are all 90°, so look at the sides: similar only if 126 and 94 are equal.
11. True
Rectangles' angles are all 90°, so look at the sides: similar only if 612 and 24 are equal.
12. A. two squares
A square's angles are all 90° and its four sides equal, so any two squares have sides in proportion: always similar.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 108 cm
Length : width = 15 : 10 = 3 : 2, so the big screen's length = 72 × 3 ÷ 2 = 108 cm.
14. 2.5, 15
Length with length: 37.5 ÷ 15 = 2.5; width = 6 × 2.5 = 15 cm.
15. True
Inside, both length and width lose 2 × 2 cm; taking the same amount off both keeps the ratio only for a square.
16. 27, 54
Perimeter 27 cm; every side times 200, so the perimeter too: 27 × 200 cm = 54 m.
17. False
Inside, both length and width lose 2 × 3 cm; taking the same amount off both keeps the ratio only for a square.
18. 29, 58
Perimeter 29 cm; every side times 200, so the perimeter too: 29 × 200 cm = 58 m.

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