Parallel and Intersecting Lines — Question 5

In the given figure, line a is parallel to line c because these two lines are always the same distance apart and never meet, no matter how far they go. Figure it Out (Page 119) 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. Solution: Tools needed: Ruler, Set-squares (right-angled triangle), Pencil Steps: Place the set square so that one side is along the line l. Hold the ruler against the other side of the set square (the ruler won’t move). Slide the set square along the ruler until one side reaches point A. Draw a line along the edge of the set square through point A. This new line is parallel to line l and passes through point A. Making Parallel Lines through Paper Folding NCERT In-Text Questions (Page 120) 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 parallel to each other. Why are lines l and m parallel to each other? Solution: Line t is perpendicular to line l; line m is also perpendicular to line t. Thus, if two lines are perpendicular to the same line, they are parallel to each other. Thus, lines l and m are parallel to each other because they share the same perpendicular relationship with line t. Figure it Out (Pages 123-125)