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Parallel and Intersecting Lines

A bend between two parallels

A bent wire runs between two parallel rails. The wire bends at O. The bend is the angle at O. How wide is the bend?

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Slide O along the dashed line. Both angles change. The bend stays their sum.

A bent path from P to Q. The angles are 50° at P and 70° at Q.
Step 1 of 5
  1. A bent path from P to Q. The angles are 50° at P and 70° at Q.
  2. Draw a dashed line through O, parallel to both rails.
  3. Alternate angles are equal. The upper part of the bend is 50°.
  4. The lower part of the bend is 70°.
  5. The whole bend is 50° + 70° = 120°.

Here P and Q are left of O. The marked angles open to the right.

The rule

Here the bend is 50° + 70° = 120°. Both ends lie on one side of O.

A path bends at O between two parallel lines. Its two ends lie on the same side of O. At each end, mark the angle that opens towards O. Draw a parallel through O. Alternate angles are equal. So the bend is the sum of the two marked angles.

Now find an end angle from the bend. Take the bend as 124° and the angle at P as 47°. Then the angle at Q is 124° − 47° = 77°.

With more bends, draw a dashed parallel through each bend. Work one bend at a time.

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This track

  1. 0 Start here
  2. 1 Cross once, or never cross
  3. 2 What parallel really means
  4. 3 The four angles at a crossing
  5. 4 Angles that fill a straight line
  6. 5 One line laid across two
  7. 6 Only when the lines are parallel
  8. 7 Finding an angle nobody measured
  9. 8 Square corners: perpendicular lines
  10. 9 Parallels from square corners
  11. 10 A bend between two parallels
  12. 11 Checkpoint: square corners and bends
  13. 12 The big picture
  14. 13 Track quiz

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