Geometry and proof · Ages 12–13
Corresponding, alternate and interior angles worksheet
Part of: Angles & parallel lines
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Corresponding, alternate and interior angles worksheet
Geometry and proof · Ages 12–13
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Choose, or true or false (2 marks each)
1.In each picture two parallel lines are cut by a transversal, one angle 45°. In which are a and b alternate angles?
- A
- B
- C
- D
Choose the right picture
Answer:
2.The two lines in the picture are parallel. What are a and b?
- A. vertically opposite angles
- B. corresponding angles
- C. alternate angles
- D. interior angles on the same side
Choose the right answer
Answer:
3.In the picture, a and b are interior angles on the same side.
True or false?
Answer:
4.In each picture two parallel lines are cut by a transversal, one angle 110°. In which are a and b alternate angles?
- A
- B
- C
- D
Choose the right picture
Answer:
5.In each picture two parallel lines are cut by a transversal, one angle 50°. In which are a and b alternate angles?
- A
- B
- C
- D
Choose the right picture
Answer:
6.In the picture, a and b are corresponding angles.
True or false?
Answer:
7.The two lines in the picture are parallel. Which angle corresponds to a?
- A. d
- B. c
- C. b
- D. e
Choose the right answer
Answer:
8.The line EF cuts AB and CD, as shown. What are ∠BEF and ∠CFE?
- A. interior angles on the same side
- B. It depends on whether AB and CD are parallel
- C. alternate angles
- D. corresponding angles
Choose the right answer
Answer:
9.The two lines in the picture are parallel. Which pair are interior angles on the same side?
- A. a and d
- B. a and b
- C. b and c
- D. a and c
Choose the right answer
Answer:
10.In each picture two lines, not necessarily parallel, are cut by a transversal, one angle 40°. In which are a and b corresponding angles?
- A
- B
- C
- D
Choose the right picture
Answer:
11.In each picture two lines, not necessarily parallel, are cut by a transversal, one angle 75°. In which are a and b corresponding angles?
- A
- B
- C
- D
Choose the right picture
Answer:
12.In each picture two lines, not necessarily parallel, are cut by a transversal, one angle 60°. In which are a and b corresponding angles?
- A
- B
- C
- D
Choose the right picture
Answer:
Part B: Word problems (4 marks each)
13.AB // CD, and the line EF cuts them at E and F, as shown. What are ∠BEF and ∠EFD?
- A. corresponding angles
- B. alternate angles
- C. interior angles on the same side
- D. adjacent angles on a straight line
Choose the right answer
Working:
Answer:
14.AB // CD, and the line EF cuts them at E and F, as shown. What are ∠AEF and ∠EFD?
- A. vertically opposite angles
- B. interior angles on the same side
- C. alternate angles
- D. corresponding angles
Choose the right answer
Working:
Answer:
15.In the picture, a and b are alternate angles.
True or false?
Working:
Answer:
16.The two lines in the picture are parallel. Which angle is alternate to a?
- A. b
- B. c
- C. d
- D. e
Choose the right answer
Working:
Answer:
17.In the picture a and b are corresponding angles, and a = 65°. Which statement is right?
- A. b must be 115°
- B. a + b must be 180°
- C. b must be 65°
- D. Only if the two lines are parallel must b be 65°
Choose the right answer
Working:
Answer:
18.In each picture two parallel lines are cut by a transversal, one angle 110°. In which are a and b interior angles on the same side?
- A
- B
- C
- D
Choose the right picture
Working:
Answer:
Show the answers and working
Corresponding, alternate and interior angles worksheet: Answers and working
Part A: Choose, or true or false
1. C
Alternate angles are on opposite sides of the transversal and both between the lines, making a Z.
2. D. interior angles on the same side
Ask: are a and b on the same side of the transversal? Then: are they between the lines? Corresponding F, alternate Z, interior C; vertically opposite at one crossing.
3. False
Interior angles on the same side are on one side of the transversal and both between the lines (a C). Check whether a and b are on one side, then whether both are between the lines.
4. A
Alternate angles are on opposite sides of the transversal and both between the lines, making a Z.
5. D
Alternate angles are on opposite sides of the transversal and both between the lines, making a Z.
6. True
Corresponding angles are on one side of the transversal, one between the lines and one outside (an F). The name depends only on place: parallel or not, it is the same.
7. C. b
a's corresponding angle is at the other crossing, on the same side of the transversal, and above its line just as a is (or below, as a is): together an F.
8. C. alternate angles
∠BEF is right of the transversal and ∠CFE left, both between AB and CD, like a Z: alternate angles. The name depends only on place, not on whether the lines are parallel.
9. B. a and b
Interior angles on the same side are on one side of the transversal and both between the lines (a C). Check each pair for both; only one pair passes.
10. C
Corresponding angles are on one side, one between the lines and one outside (an F). They are corresponding even when the lines aren't parallel; they just needn't be equal.
11. A
Corresponding angles are on one side, one between the lines and one outside (an F). They are corresponding even when the lines aren't parallel; they just needn't be equal.
12. D
Corresponding angles are on one side, one between the lines and one outside (an F). They are corresponding even when the lines aren't parallel; they just needn't be equal.
Part B: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. C. interior angles on the same side
∠BEF and ∠EFD are both right of the transversal and both between AB and CD, like a C: interior angles on the same side.
14. C. alternate angles
∠AEF is left of the transversal and ∠EFD right, both between AB and CD, making a Z: alternate angles.
15. False
Alternate angles are on opposite sides of the transversal and both between the lines (a Z). Check which side a and b are on, then whether both are between the lines.
16. D. e
a is between the lines. Its alternate angle is on the other side of the transversal, also between the lines, at the other crossing: together a Z.
17. D. Only if the two lines are parallel must b be 65°
"Corresponding" names a position only, parallel or not. Only when the lines are parallel are corresponding angles equal.
18. C
Interior angles on the same side are on one side of the transversal and both between the lines, like a C.
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