Geometry and proof · Ages 14–15

Corresponding sides of similar triangles worksheet

Part of: Similar triangles

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Geometry and proof · Ages 14–15

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

1.△ABC ~ △DEF, AB = 4 cm, BC = 5 cm and DE = 8 cm. EF =
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2.In the picture, △ABC ~ △PQR. x =
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3.△ABC ~ △DEF, AB = 9 cm, BC = 6 cm and DE = 27 cm. EF =
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4.△ABC ~ △DEF, AB = 5 cm, BC = 3 cm and DE = 20 cm. EF =
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5.In the picture, △ABC ~ △XYZ. x = , y =
Fill in each blank
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6.The two triangles in the picture are similar; equal angles carry the same marks. x =
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7.△ABC ~ △PQR with AB : PQ = 3 : 4. The perimeter of △ABC is 39 cm. The perimeter of △PQR =
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8.△ABC ~ △PQR, with AB = 7 cm, BC = 8 cm and PQ = 8 cm. QR = cm (as a fraction)
Answer in simplest form
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9.△ABC ~ △PQR, with AB = 8 cm, BC = 10 cm and PQ = 14 cm. QR = cm (as a fraction)
Answer in simplest form
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10.△ABC ~ △PQR with AB : PQ = 2 : 5. The perimeter of △ABC is 24 cm. The perimeter of △PQR =
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13.On a plan, a triangular road sign has sides of 6 cm, 8 cm and 10 cm. The real sign is similar to the plan, its longest side 110 cm. How long is its shortest side?
Working:
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14.In the sun, a 2 m pole standing upright casts a shadow 3 m long; at the same moment a tree beside it casts a shadow of 18 m. The pole and its shadow and the tree and its shadow make similar triangles. Tree's shadow ÷ pole's shadow = , so the tree is m tall.
Fill in each blank
Working:
Answer:
15.Two triangular flags have the same shape. The small one's sides are 13 cm, 22 cm and 26 cm, and the big one's shortest side is 19.5 cm. Scale = , and the big flag's perimeter = cm.
Fill in each blank
Working:
Answer:
16.A model car has the same shape as the real one. The model is 17 cm long and 3 cm wide; the real car is 204 cm long. The real car is times as long as the model, and cm wide.
Fill in each blank
Working:
Answer:
17.A model car has the same shape as the real one. The model is 13 cm long and 8 cm wide; the real car is 130 cm long. The real car is times as long as the model, and cm wide.
Fill in each blank
Working:
Answer:
18.In the sun, a 2 m pole standing upright casts a shadow 4 m long; at the same moment a tree beside it casts a shadow of 24 m. The pole and its shadow and the tree and its shadow make similar triangles. Tree's shadow ÷ pole's shadow = , so the tree is m tall.
Fill in each blank
Working:
Answer:

Show the answers and working

Corresponding sides of similar triangles worksheet: Answers and working

1. 10 cm
DE goes with AB: the scale is 8 ÷ 4 = 2; EF goes with BC: EF = 5 × 2 = 10 cm.
2. 10 cm
PQ ÷ AB = 6 ÷ 3 = 2; QR goes with BC: x = 5 × 2 = 10 (corr. sides, ~△s).
3. 18 cm
DE goes with AB: the scale is 27 ÷ 9 = 3; EF goes with BC: EF = 6 × 3 = 18 cm.
4. 12 cm
DE goes with AB: the scale is 20 ÷ 5 = 4; EF goes with BC: EF = 3 × 4 = 12 cm.
5. 3, 3
Scale = XY ÷ AB = 4 ÷ 8 = 0.5: x = 6 × 0.5 = 3, y = 6 × 0.5 = 3.
6. 7.5 cm
Match the corners by their marks: the 7 cm side goes with the 10.5 cm side, a scale of 10.5 ÷ 7 = 1.5; x goes with 5 cm: x = 5 × 1.5 = 7.5.
7. 52 cm
Every side is multiplied by 43, so their sum is too: 39 × 4 ÷ 3 = 52 cm.
8. 647
QRBC = PQAB: QR8 = 87, so QR = 8 × 8 ÷ 7 = 647.
9. 352
QRBC = PQAB: QR10 = 148, so QR = 10 × 14 ÷ 8 = 352.
10. 60 cm
Every side is multiplied by 52, so their sum is too: 24 × 5 ÷ 2 = 60 cm.

11. B. 21 cm
A goes with P, B with R, C with Q. The scale is PR ÷ AB = 27 ÷ 9 = 3, and QR goes with BC: 7 × 3 = 21 cm.
12. C. 18 cm
A goes with P, B with R, C with Q. The scale is PR ÷ AB = 21 ÷ 7 = 3, and QR goes with BC: 6 × 3 = 18 cm.

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

13. 66 cm
Longest with longest: scale = 110 ÷ 10 = 11; shortest = 6 × 11 = 66 cm.
14. 6, 12
The sun's rays meet the ground at one angle, so the right triangles are similar: scale = 18 ÷ 3 = 6, tree = 2 × 6 = 12 m.
15. 1.5, 91.5
Shortest with shortest: 19.5 ÷ 13 = 1.5; the perimeter is multiplied by 1.5 too: (13 + 22 + 26) × 1.5 = 91.5 cm.
16. 12, 36
Scale = 204 ÷ 17 = 12; the width is multiplied by 12 too: 3 × 12 = 36 cm.
17. 10, 80
Scale = 130 ÷ 13 = 10; the width is multiplied by 10 too: 8 × 10 = 80 cm.
18. 6, 12
The sun's rays meet the ground at one angle, so the right triangles are similar: scale = 24 ÷ 4 = 6, tree = 2 × 6 = 12 m.

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