Geometry and proof · Ages 13–14

Corresponding parts of congruent triangles worksheet

Part of: Congruent triangles

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Geometry and proof · Ages 13–14

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

1.In the picture, △ABC ≅ △QRP. x =
Answer:
2.In the picture, △ABC ≅ △PQR. x =
Answer:
3.The two triangles are congruent; sides with the same marks are equal. x = , y = .
Fill in each blank
Answer:
4.△ABC ≅ △PQR, ∠A = 64° and ∠Q = 30°. ∠R =
Answer:
5.△ABC ≅ △PQR, ∠A = 90° and ∠Q = 30°. ∠R =
Answer:
6.The two triangles are congruent; sides with the same marks are equal. x =
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7.△ABC ≅ △QRP, AB = 4 cm and RP = 10 cm, and the perimeter of △QRP is 22 cm. PQ =
Answer:

13.△ABC ≅ △DEF, ∠A = 34° and ∠E = 62°. ∠D = °, ∠F = °.
Fill in each blank
Working:
Answer:
14.△PQR ≅ △LMN, PQ = 10 cm, QR = 13 cm and PR = 15 cm. So LN = 10 cm.
True or false?
Working:
Answer:
15.Two triangular pieces of card are congruent, and angles with the same marks are equal, as shown. Which is written correctly?
- A. △ABC ≅ △XZY
- B. △ABC ≅ △YXZ
- C. △ABC ≅ △ZYX
- D. △ABC ≅ △XYZ
Choose the right answer
Working:
Answer:
16.Two congruent triangular pieces of card; angles with the same marks are equal, as shown. x =
Working:
Answer:
17.Two congruent triangular boards: △ABC ≅ △XYZ. AB = 10 cm, BC = 12 cm and CA = 17 cm. How long is YZ?
Working:
Answer:
18.△ABC ≅ △DEF, ∠A = 72° and ∠E = 44°. ∠D = °, ∠F = °.
Fill in each blank
Working:
Answer:

Show the answers and working

Corresponding parts of congruent triangles worksheet: Answers and working

1. 8 cm
Match the letters in order: A with Q, B with R, C with P. The side marked x goes with the 8 cm side of △ABC (corr. sides, ≅△s).
2. 4 cm
Match the letters in order: A with P, B with Q, C with R. The side marked x goes with the 4 cm side of △ABC (corr. sides, ≅△s).
3. 8, 5
Sides with the same marks correspond and are equal (corr. sides, ≅△s): x = 8, y = 5.
4. 86°
∠P = ∠A = 64° (corr. ∠s, ≅△s), so ∠R = 180° − 64° − 30° = 86° (∠ sum of △).
5. 60°
∠P = ∠A = 90° (corr. ∠s, ≅△s), so ∠R = 180° − 90° − 30° = 60° (∠ sum of △).
6. 75°
Match by the side marks: A with P, B with Q, C with R. ∠A = ∠P = 58° (corr. ∠s, ≅△s), so x = ∠C = 180° − 58° − 47° = 75° (∠ sum of △).
7. 8 cm
A goes with Q, B with R, C with P: QR = AB = 4 cm (corr. sides, ≅△s). The perimeter of △QRP is QR + RP + PQ, so PQ = 22 − 4 − 10 = 8 cm.

8. True
AB is the first and second letters, so it goes with PQ: PQ = AB = 12 cm (corr. sides, ≅△s); BC goes with QR.
9. C. AB = PR
In order: A ↔ P, B ↔ R, C ↔ Q, so AB = PR (corr. sides, ≅△s).
10. B. △ABC ≅ △PQR
Sides with the same marks correspond, and so do the vertices they face; in a ≅ statement, corresponding vertices go in the same places.
11. D. ∠Q
∠C = 180° − 58° − 79° = 43°. ∠P = ∠A = 58°, ∠Q = ∠B = 79°, ∠R = ∠C = 43° (corr. ∠s, ≅△s).
12. D. ∠R
∠C = 180° − 67° − 42° = 71°. ∠P = ∠A = 67°, ∠Q = ∠B = 42°, ∠R = ∠C = 71° (corr. ∠s, ≅△s).

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

13. 34, 84
∠D = ∠A = 34° (corr. ∠s, ≅△s), ∠F = 180° − 34° − 62° = 84° (∠ sum of △).
14. False
L goes with P and N with R, so LN goes with PR: LN = 15 cm (corr. sides, ≅△s).
15. D. △ABC ≅ △XYZ
Corners with the same marks correspond; in a ≅ statement, corresponding vertices go in the same places.
16. 81°
x goes with the unmarked ∠A: x = ∠A = 180° − 41° − 58° = 81° (corr. ∠s, ≅△s; ∠ sum of △).
17. 12 cm
Y goes with B and Z with C, so YZ goes with BC: YZ = 12 cm (corr. sides, ≅△s).
18. 72, 64
∠D = ∠A = 72° (corr. ∠s, ≅△s), ∠F = 180° − 72° − 44° = 64° (∠ sum of △).

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