Angles & parallel lines · Ages 12–13
Telling parallel lines
Corr. equal, alt. equal, or int. adding to 180°.
How to do it
Method
Corr. equal, alt. equal, or int. adding to 180°
∠AEF = ∠EFD = 65°, so AB // CD (alt. ∠s equal)
Another way
Turn it into another relation
70° + 110° = 180°, or 180° − 110° = 70°
In full
Two lines are parallel when any one of these holds: corresponding angles are equal (reason: corr. ∠s equal); alternate angles are equal (reason: alt. ∠s equal); interior angles on the same side add up to 180° (reason: int. ∠s supp.). Careful: interior angles must add to 180°, not be equal. And look at which angles: ∠AEF and ∠BEF are at one point and always add to 180°, so they prove nothing. Looking parallel doesn't count; the angles must show it. Another way: turn one relation into another. Interior angles of 70° and 110°: the 110° makes a straight line with an alternate angle of 70°, so the alternate angles are both 70°, and the lines are parallel.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
The line EF cuts AB and CD, as shown, and ∠AEF = 70°. If AB // CD, ∠EFD = ° and ∠EFC = °.
Fill in each blank
Show the answer and working
Answer: 70, 110
∠EFD = ∠AEF = 70° (alt. ∠s, AB // CD); ∠EFC = 180° − 70° = 110° (int. ∠s, AB // CD).
Example 2
For the two lines in the picture to be parallel, x =
Show the answer and working
Answer: 65°
See where x is from 115°: corresponding or alternate angles must be equal (corr. ∠s equal, alt. ∠s equal), interior ones must add to 180° (int. ∠s supp.). Here x = 65°.
Example 3
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 add to 180°
- C. Parallel: the interior angles are equal
- D. Not parallel: the interior angles don't add to 180°
Choose the right answer
Show the answer and working
Answer: B. Parallel: the interior angles 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.): 105° + 75° = 180°.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Two angles are marked in the picture. By which reason are the two lines parallel?
- A. alt. ∠s equal
- B. corr. ∠s equal
- C. int. ∠s supp.
- D. vert. opp. ∠s
Choose the right answer
Answer:
2.The line EF cuts AB and CD, as shown, and ∠AEF = 110°. If AB // CD, ∠EFD = ° and ∠EFC = °.
Fill in each blank
Answer:
3.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:
4.For the two lines in the picture to be parallel, what must x be?
Answer:
5.The line EF cuts AB and CD, as shown. Which of these does NOT prove AB // CD?
- A. ∠AEF = 40°, ∠BEF = 140°
- B. ∠BEF = 140°, ∠EFD = 40°
- C. ∠BEF = 140°, ∠CFE = 140°
- D. ∠AEF = 40°, ∠EFD = 40°
Choose the right answer
Answer:
All the answers
- 1. A. alt. ∠s equal
- 2. 110, 70
- 3. True
- 4. 140°
- 5. A. ∠AEF = 40°, ∠BEF = 140°
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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