Angles at parallel lines: a road crossing two canals
A straight road crosses two parallel canals. Mark one angle where it meets the first canal, then find its vertically opposite angle, its linear pair, and the corresponding, alternate and co-interior angles at the second canal.
Core concept
When a transversal cuts two parallel lines, vertically opposite, corresponding and alternate angles are equal, while a linear pair and co-interior angles add up to 180°
Topic: Lines and angles
Two canals run side by side, always the same distance apart: they are parallel lines. A straight road crosses both; a line that cuts two lines like this is a transversal. It makes four angle: The amount of turn between two lines that meet, measured in degrees (°). All key words at each canal. Some pairs of these angles are always equal and some always add up to 180°. Vertically opposite angles face each other across a crossing and are equal. Two angles side by side on a straight line are a linear pair and add up to 180°. Corresponding angles sit in the same position at the two canals; alternate angles lie between the canals on opposite sides of the road; both pairs are equal. Co-interior angles lie between the canals on the same side of the road and add up to 180°.
What you will learn
- Name vertically opposite angles, linear pairs, and corresponding, alternate and co-interior angles.
- Find an unknown angle from a known one.
- Know which pairs are equal and which add up to 180°.
Before you start
- Know that the angles on a straight line add up to 180°.
Materials
- A ruler, a pencil and a protractor
Equipment
- Lined paper (its lines are parallel)
Procedure
- Record the vertically opposite angle of 60°.
- Record its linear pair.
- Record its corresponding and alternate angles.
- Record co-interior angles for a different marked angle.
How this simulation is simplified
- The two canals are exactly parallel and the road is a straight line.