Geometry and proof · Ages 13–14

Congruent figures and transformations worksheet

Part of: Congruent triangles

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Geometry and proof · Ages 13–14

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

1.△A′B′C′ is the image of △ABC after a transformation, as shown, and the two are congruent. A′B′ is units long.
Answer:
2.△ABC is reflected to give △A′B′C′. ∠A = 85° and ∠B = 54°. ∠C′ =
Answer:
3.△ABC is reflected to give △A′B′C′, then △A′B′C′ is enlarged 2 times to give △A″B″C″. AB = 8 cm, the perimeter of △ABC is 22 cm, and ∠B = 119°. A″B″ = cm, the perimeter of △A″B″C″ = cm, and ∠B″ = °.
Fill in each blank
Answer:
4.△ABC turned 90° about the origin gives △A′B′C′, as shown. A′B′ = units, A′C′ = units, and the area of △A′B′C′ = square units.
Fill in each blank
Answer:
5.△ABC is reflected to give △A′B′C′, then △A′B′C′ is enlarged 3 times to give △A″B″C″. AB = 8 cm, the perimeter of △ABC is 19 cm, and ∠B = 40°. A″B″ = cm, the perimeter of △A″B″C″ = cm, and ∠B″ = °.
Fill in each blank
Answer:

6.After which of these transformations is the image not congruent to the figure?
- A. an enlargement, 3 times
- B. a reflection
- C. a rotation
- D. a translation
Choose the right answer
Answer:
7.The blue triangle is the image of the orange one after a transformation. The two triangles are congruent.
True or false?
Answer:
8.A square of side 5 cm is transformed, and its image has sides of 5 cm. The transformation could be a rotation.
True or false?
Answer:
9.Which transformation takes the orange triangle to the blue one?
- A. a rotation
- B. an enlargement
- C. a translation
- D. a reflection
Choose the right answer
Answer:
10.A square of side 8 cm is transformed, and its image has sides of 16 cm. The transformation could be a rotation.
True or false?
Answer:
11.A rectangle has sides of 7 cm and 11 cm. After one transformation, its image is a rectangle with sides of 9 cm and 9 cm. The transformation could be a rotation.
True or false?
Answer:
12.A rectangle has sides of 12 cm and 5 cm. After one transformation, its image is a rectangle with sides of 12 cm and 5 cm. The transformation could be a rotation.
True or false?
Answer:

13.△ABC is reflected to give △A′B′C′. The area of △ABC is 12 cm². The area of △A′B′C′ =
Working:
Answer:
14.Which of these about congruent figures is right?
- A. An enlarged figure is congruent to the original
- B. Two figures with equal areas must be congruent
- C. Congruent figures always face the same way
- D. A reflected figure is congruent to the original
Choose the right answer
Working:
Answer:
15.A triangular tile has sides of 17 cm, 18 cm and 20 cm. It is turned and laid beside where it was. What is the image's perimeter?
Working:
Answer:
16.The blue rectangle is the image of the orange one after a transformation. The two rectangles are congruent.
True or false?
Working:
Answer:
17.△ABC is translated to △PQR (A to P, B to Q, C to R). AB = 8 cm, ∠B = 66° and ∠C = 79°. PQ = cm, ∠P = °.
Fill in each blank
Working:
Answer:
18.△ABC is reflected to give △A′B′C′. The area of △ABC is 9 cm². The area of △A′B′C′ =
Working:
Answer:

Show the answers and working

Congruent figures and transformations worksheet: Answers and working

1. 2
Corresponding sides of congruent figures are equal: A′B′ = AB = 2 units.
2. 41°
The reflected image is congruent to the figure: ∠C′ = ∠C = 180° − 85° − 54° = 41°.
3. 16, 44, 119
The reflection keeps it congruent: A′B′ = 8 cm and ∠B′ = 119°. Enlarged 2 times, every side becomes 2 times as long: A″B″ = 2 × 8 = 16 cm, and the perimeter = 2 × 22 = 44 cm; but the shape stays the same, so the angles don't grow: ∠B″ = 119°. So △A″B″C″ is not congruent to △ABC.
4. 2, 3, 3
The turned image is congruent: A′B′ = AB = 2, A′C′ = AC = 3, and its area = 2 × 3 ÷ 2 = 3.
5. 24, 57, 40
The reflection keeps it congruent: A′B′ = 8 cm and ∠B′ = 40°. Enlarged 3 times, every side becomes 3 times as long: A″B″ = 3 × 8 = 24 cm, and the perimeter = 3 × 19 = 57 cm; but the shape stays the same, so the angles don't grow: ∠B″ = 40°. So △A″B″C″ is not congruent to △ABC.

6. A. an enlargement, 3 times
Enlarged 3 times, every side becomes 3 times as long: the same shape, a different size, so not congruent.
7. True
A translation, reflection or rotation keeps size and shape, so the image is congruent; an enlargement changes the lengths, so it isn't. Count the sides on the grid to see.
8. True
A rotation keeps the size, so the image's sides must stay 5 cm.
9. A. a rotation
Compare lengths first: changed means an enlargement; unchanged, flipped means a reflection, turned a rotation, and only moved a translation.
10. False
A rotation keeps the size, so the image's sides must stay 8 cm.
11. False
A rotation keeps size and shape: the image's sides must still be 7 cm and 11 cm, in either order. The same perimeter or the same area alone doesn't make it congruent.
12. True
A rotation keeps size and shape: the image's sides must still be 12 cm and 5 cm, in either order. The same perimeter or the same area alone doesn't make it congruent.

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

13. 12 cm²
The reflected image is congruent, so its area is unchanged: 12 cm².
14. D. A reflected figure is congruent to the original
A reflection changes only the direction, not size or shape, so the image is congruent.
15. 55 cm
A turned image is congruent, its sides unchanged: 17 + 18 + 20 = 55 cm.
16. True
Count each rectangle's length and width on the grid: all the same means congruent; one different means not.
17. 8, 35
The translated image is congruent: PQ = AB = 8 cm, ∠P = ∠A = 180° − 66° − 79° = 35°.
18. 9 cm²
The reflected image is congruent, so its area is unchanged: 9 cm².

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