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Chapter 5: Parallel and Intersecting Lines

    Across the Line

    Perpendicular Lines

    Between Lines

    Parallel and Perpendicular Lines in Paper Folding

    Transversals

    Corresponding Angles

    Drawing Parallel Lines

    Alternate Angles

    Parallel Illusions

    Summary

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Glossary

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Chapter 5: Parallel and Intersecting Lines > Drawing Parallel Lines

Drawing Parallel Lines

Can you draw a pair of parallel lines using a ruler and a set square? The figure below shows how you can do it.

Draw a line l with a scale. By sliding your set square you can make two lines to line l.

Are these two lines parallel to each other? How are we sure that they are parallel to each other? What angles are formed between these lines and line l?

Since we used a set square, the angles measure °. The position of the lines is different, but they make the same angle with l. If line l is seen as a to the two new lines, then the corresponding angles measure °.

As we know these are corresponding angles and they are equal, we can be sure that the lines are .

Draw two more parallel lines using the long side of the set square as shown above.

How do you know these two lines are parallel? We have used the same edge and the same set-square orientation for making both the lines.

Can you check if the corresponding angles are equal?

Figure it Out

Can you draw a line parallel to l, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.

Tools needed: Ruler, Set square, Pencil
Method 1: Using a Set Square and Ruler
Position the ruler along line l so that it's aligned with the line. Place a set square against the ruler with one edge touching the ruler. Hold the ruler firmly in place.
Slide the set square along the ruler (keeping it pressed against the ruler) until its other edge passes through point A.
Draw the line along the edge of the set square that passes through point A.
This line will be parallel to line l because the set square maintains a angle as it slides along the ruler.
Method 2: Using Two Set Squares
Place the first set square along line l. Place the second set square against an edge of the first set square. Hold the second set square firmly
Slide the first set square along the edge of the second set square until it reaches point A.
Draw the line through point A along the edge of the first set square.

Making Parallel Lines through Paper Folding

Let us try to do the same with paper folding. For a line l (given as a crease), how do we make a line parallel to l such that it passes through point A?

We know how to fold a piece of paper to get a line perpendicular to l. Now, try to fold a perpendicular to l such that it passes through point A. Let us call this new crease t.

Now, fold a line perpendicular to t passing through A again. Let us call this line m. The lines l and m are to each other.

Why are lines l and m parallel to each other? Because they are to the line i.e.