Geometry and proof · Ages 12–13

Telling parallel lines worksheet

Part of: Angles & parallel lines

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Geometry and proof · Ages 12–13

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.The line EF cuts AB and CD, as shown, and ∠AEF = 50°. If AB // CD, ∠EFD = ° and ∠EFC = °.
Fill in each blank
Answer:
2.The line EF cuts AB and CD, as shown, and ∠AEF = 140°. If AB // CD, ∠EFD = ° and ∠EFC = °.
Fill in each blank
Answer:
3.The line EF cuts AB and CD, as shown, and ∠AEF = 70°. If AB // CD, ∠EFD = ° and ∠EFC = °.
Fill in each blank
Answer:
4.For the two lines in the picture to be parallel, x =
Answer:
5.For the two lines in the picture to be parallel, what must x be?
Answer:

6.Two angles are marked in the picture. By which reason are the two lines parallel?
- A. int. ∠s supp.
- B. alt. ∠s equal
- C. corr. ∠s equal
- D. vert. opp. ∠s
Choose the right answer
Answer:
7.The two marked angles are corresponding angles. The two lines are parallel.
True or false?
Answer:
8.The two marked angles are on one side of the transversal. Are the two lines parallel? Why?
- A. Not parallel: the interior angles aren't equal
- B. Parallel: the interior angles are equal
- C. Parallel: the interior angles add to 180°
- D. Not parallel: the interior angles don't add to 180°
Choose the right answer
Answer:
9.Two lines are cut by a transversal, and a pair of interior angles on the same side are both 70°. The two lines are parallel.
True or false?
Answer:
10.Two lines are cut by a transversal, and a pair of interior angles on the same side are both 90°. The two lines are parallel.
True or false?
Answer:
11.Two lines are cut by a transversal, and a pair of interior angles on the same side are both 110°. The two lines are parallel.
True or false?
Answer:
12.The line EF cuts AB and CD, as shown. Which of these does NOT prove AB // CD?
- A. ∠AEF = 100°, ∠BEF = 80°
- B. ∠BEF = 80°, ∠CFE = 80°
- C. ∠BEF = 80°, ∠EFD = 100°
- D. ∠AEF = 100°, ∠EFD = 100°
Choose the right answer
Answer:

13.Two wooden strips are cut by a slanting strip; the interior angles on one side are 93° and 90° (if already parallel, the answer is 0). At least how many degrees must the lower strip turn to make them parallel?
Working:
Answer:
14.The line EF cuts AB and CD, as shown. ∠AEF = ∠EFD = 120°, so AB // CD (______). Which reason goes in the blank?
- A. int. ∠s supp.
- B. vert. opp. ∠s
- C. alt. ∠s equal
- D. corr. ∠s equal
Choose the right answer
Working:
Answer:
15.A line EF cuts AB at E and CD at F. ∠AEF = (2x + 11)° and ∠EFD = (3x − 17)°. For AB // CD, what is x?
Working:
Answer:
16.A line EF cuts AB at E and CD at F; ∠BEF = (x + 38)° and ∠DFE = (2x + 34)°. For AB // CD: (x + 38) + (2x + 34) = 180 (int. ∠s supp.), x = , ∠DFE = °.
Fill in each blank
Working:
Answer:
17.The line EF cuts AB and CD, as shown. ∠BEF + ∠EFD = 135° + 45° = 180°, so AB // CD (______). Which reason goes in the blank?
- A. alt. ∠s equal
- B. corr. ∠s equal
- C. int. ∠s supp.
- D. adj. ∠s on st. line
Choose the right answer
Working:
Answer:
18.A road crosses two rails, and a pair of alternate angles are 104° and 102°. The rails are parallel.
True or false?
Working:
Answer:

Show the answers and working

Telling parallel lines worksheet: Answers and working

1. 50, 130
∠EFD = ∠AEF = 50° (alt. ∠s, AB // CD); ∠EFC = 180° − 50° = 130° (int. ∠s, AB // CD).
2. 140, 40
∠EFD = ∠AEF = 140° (alt. ∠s, AB // CD); ∠EFC = 180° − 140° = 40° (int. ∠s, AB // CD).
3. 70, 110
∠EFD = ∠AEF = 70° (alt. ∠s, AB // CD); ∠EFC = 180° − 70° = 110° (int. ∠s, AB // CD).
4. 130°
See where x is from 50°: corresponding or alternate angles must be equal (corr. ∠s equal, alt. ∠s equal), interior ones must add to 180° (int. ∠s supp.). Here x = 130°.
5. 125°
The angle corresponding to 55° sits beside x and must be 55° (corr. ∠s equal); it lies on a straight line with x, so x = 180° − 55° = 125° (adj. ∠s on st. line).

6. A. int. ∠s supp.
Place first: corresponding F, alternate Z, interior C; then size: corresponding or alternate angles equal, or interior ones adding to 180°, make the lines parallel. Here they are 70° and 110°.
7. True
The lines are parallel only if corresponding angles are equal (corr. ∠s equal). Here they are 50° and 50°.
8. D. Not parallel: the interior angles don't add to 180°
The two are on one side, both between the lines: interior angles. The lines are parallel only if they add to 180° (int. ∠s supp.): 100° + 83° = 183°.
9. False
The lines are parallel only if interior angles add to 180° (int. ∠s supp.): 70° + 70° = 140°. That happens only when both are 90°.
10. True
The lines are parallel only if interior angles add to 180° (int. ∠s supp.): 90° + 90° = 180°. That happens only when both are 90°.
11. False
The lines are parallel only if interior angles add to 180° (int. ∠s supp.): 110° + 110° = 220°. That happens only when both are 90°.
12. A. ∠AEF = 100°, ∠BEF = 80°
∠AEF and ∠BEF share a point on the line AB, so they add to 180° whether or not AB // CD (adj. ∠s on st. line): they prove nothing.

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

13. 3°
When parallel, interior angles add to 180°. Now 93° + 90° = 183°, 3° away from 180°, so it must turn 3°.
14. C. alt. ∠s equal
∠AEF and ∠EFD are on opposite sides, both between the lines: alternate angles. Alternate angles are equal, so AB // CD.
15. 28
∠AEF and ∠EFD are alternate, so they must be equal: 2x + 11 = 3x − 17, x = 11 + 17, x = 28. Both are then 67°.
16. 36, 106
∠BEF and ∠DFE are interior angles, so they must add to 180: 3x + 38 + 34 = 180, x = 36; ∠DFE = 2 × 36 + 34 = 106°.
17. C. int. ∠s supp.
∠BEF and ∠EFD are on one side, both between the lines: interior angles. They add to 180°, so AB // CD (int. ∠s supp.).
18. False
Lines are parallel only if alternate angles are equal. Equal 104° and 102° mean parallel; even 1° apart, they aren't.

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