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Lesson · Grade 11 · Foundations of Mathematics

Angles made by parallel lines and a transversal

  • Grade 11
  • Foundations of Mathematics
  • 1 min 58 s
  • British Columbia
  • BC11-MA-24

Two parallel lines are cut by a transversal at 65°, and the angle rules fill in all eight angles one at a time: vertically opposite, corresponding (F) and alternate interior (Z) angles are 65°, co-interior (C) angles add to 180°, and each of the other angles is 180° − 65° = 115°. A two-step problem then finds x = 115° using vertically opposite and then co-interior angles, and tilting one line shows the common mistake: the corresponding angle becomes 50°, not 65°, so the F, Z and C rules need parallel lines.

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In one sentence

The question this lesson answers

Parallel lines never meet. Arrow marks show that two lines are parallel.

A transversal is a line that crosses both, making four angles at each crossing.

Transcript

What the lesson says

Parallel lines never meet. Arrow marks show that two lines are parallel.

A transversal is a line that crosses both, making four angles at each crossing.

One angle is 65 degrees. Can we find the other seven?

Vertically opposite angles face each other at a crossing, and are equal. So this one is 65 degrees.

Corresponding angles are in the same position at each crossing, in an F shape. On parallel lines, they are equal.

Alternate interior angles are between the lines, on opposite sides of the transversal, in a Z shape. They are equal too.

Co-interior angles are between the lines on the same side, in a C shape. They add up to 180 degrees.

So this angle is 180 minus 65, which is 115 degrees.

The last three each sit on a straight line with a 65 degree angle, so each is 115 degrees.

Now a two-step problem: from the 65 degree angle alone, find x.

Step 1: vertically opposite angles are equal, so this angle is 65 degrees.

Step 2: it and x are co-interior, so x is 180 minus 65, which is 115 degrees, as we found earlier.

A common mistake is using F, Z and C on lines that are not parallel. Tilt one line, and the corresponding angle becomes 50 degrees, not 65.

With parallel lines, corresponding and alternate interior angles are equal, and co-interior angles add up to 180 degrees.

Curriculum

Where this fits

British Columbia, Grade 11

Foundations of Mathematics 11, Geometry: angle relationshipsBC11-MA-24

Next: Proving the angle sums of triangles and polygons

The outcomes and strands follow the British Columbia curriculum.

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