Shape and space · Ages 9–10

Congruent shapes worksheet

Part of: Coordinates and moving shapes

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Shape and space · Ages 9–10

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.Shapes P and Q are congruent, and each square is 1 cm². What is the area of Q in cm²?
Answer:
2.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 8 cm, BC = 9 cm and CA = 3 cm. How long is EF in cm?
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3.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 4 cm, BC = 7 cm and CA = 8 cm. How long is EF in cm?
Answer:
4.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 9 cm, BC = 5 cm and CA = 6 cm. How long is EF in cm?
Answer:
5.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 7 cm, BC = 5 cm and CA = 9 cm. How long is EF in cm?
Answer:
6.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 9 cm, BC = 7 cm and CA = 4 cm. How long is EF in cm?
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7.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 6 cm, BC = 3 cm and CA = 5 cm. How long is EF in cm?
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8.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 9 cm, BC = 7 cm and CA = 5 cm. How long is EF in cm?
Answer:
9.Triangles ABC and DEF are congruent, with A matching D, B matching E and C matching F. AB = 9 cm, BC = 5 cm and CA = 7 cm. How long is EF in cm?
Answer:

13.Ming uses a rectangular stamp 6 cm long and 3 cm wide, stamping 2 times. The prints are all congruent and don't overlap. What area do they cover in all, in cm²?
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14.Mooncakes pressed from the same mould are all congruent. Each is 8 cm across. 2 of them are set in a row, each touching the next. How long is the row in cm?
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15.Two cardboard triangles are congruent. One has sides of 9 cm, 4 cm and 9 cm. What is the perimeter of the other in cm?
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16.Tsz-ching lays 2 congruent rectangular cards side by side, long side against long side, to make one big rectangle. Each card is 6 cm long and 4 cm wide. What is the big rectangle's perimeter in cm?
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17.Mooncakes pressed from the same mould are all congruent. Each is 5 cm across. 8 of them are set in a row, each touching the next. How long is the row in cm?
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18.Two cardboard triangles are congruent. One has sides of 3 cm, 4 cm and 5 cm. What is the perimeter of the other in cm?
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Show the answers and working

Congruent shapes worksheet: Answers and working

1. 4 cm²
Congruent shapes have the same area, so find P's. Count the squares along its two sides by the right angle.
Congruent shapes have the same area: P's sides by the right angle are 2 and 4, so its area is 2 × 4 ÷ 2 = 4.
2. 9 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 9 cm.
3. 7 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 7 cm.
4. 5 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 5 cm.
5. 5 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 5 cm.
6. 7 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 7 cm.
7. 3 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 3 cm.
8. 7 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 7 cm.
9. 5 cm
EF runs from E to F. Which corners of ABC do E and F match?
E matches B and F matches C, so EF matches BC: EF = 5 cm.

10. D
Count the squares along the two sides by the right angle above, then look for the same two in each picture.
A congruent triangle fits exactly once turned or flipped: its sides by the right angle are still 1 and 4 squares.
11. False
Count the squares along both sides by the right angle in P and in Q, and see if they pair up.
Turn Q round and see whether its sides by the right angle pair up with P's 1 and 2 squares.
12. D. No move of P makes it (not congruent)
Count the squares along the sides first to see if Q is P's size; then look at which way Q faces.
Compare the size first (the squares along the sides), then the way it faces: the same way is a slide, flipped is a reflection, turned round is a rotation.

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

13. 36 cm²
Every print is the same size as the stamp. Find the stamp's area first, then think about 2 of them.
Each print is congruent to the stamp, area 6 × 3; 2 of them: 2 × 6 × 3 = 36.
14. 16 cm
The mooncakes touch with no gaps. How many mooncake widths make up the row?
Each mooncake is the same size: 2 × 8 = 16 cm.
15. 22 cm
Congruent triangles have matching sides the same length, so the other one's perimeter equals this one's.
Congruent shapes have matching sides equal, so the same perimeter: 9 + 4 + 9 = 22.
16. 28 cm
Work out the big rectangle's length and width first: with the long sides together, which way doubles?
The big rectangle is 6 long and 4 + 4 = 8 wide: perimeter 2 × (6 + 8) = 28.
17. 40 cm
The mooncakes touch with no gaps. How many mooncake widths make up the row?
Each mooncake is the same size: 8 × 5 = 40 cm.
18. 12 cm
Congruent triangles have matching sides the same length, so the other one's perimeter equals this one's.
Congruent shapes have matching sides equal, so the same perimeter: 3 + 4 + 5 = 12.

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