In this workbook we will investigate the relationship between angles that are formed when a line intersects two parallel lines. [br][br]For each task below, use the applets to help you answer the corresponding questions.
In the below applet, the two lines are [i]parallel.[/i] Move the points on the lines to investigate what it means for two lines to be parallel, and then answer the questions that follow.
In your own words, describe what we mean by [i]parallel lines?[/i]
Two lines are parallel when they never intersect no matter how far you extend them[br]There is a constant distance between them.
In the below applet, two parallel lines are intersected by a third line (known as a transversal line). Some angles are therefore formed, use the applet to investigate these angles.
What do you notice about the blue angles?
What do you notice about the red angles?
The pair of blue and red angles are what we call [i]corresponding angles.[br][/i][size=150][size=200][i]Corresponding angles are always equal.[/i][/size][/size][br]The brown angle is not corresponding with the blue angles. Although they are equal, they lie on different sides of the intersecting line.
In your own words, describe what it means for two angles to be corresponding.
When a line intersects a pair of parallel lines, corresponding angles are formed. These are two angles on the same side of the intersecting line and in the same position relative to the parallel lines.
Consider the below diagram.
Which of the following three pairs of angles are [b]all[/b] corresponding angles?
For each diagram, decide whether the angles are corresponding angles or not.
Select all diagrams in the above applet which show corresponding angles
Consider the below diagram.
Which angle is corresponding to angle [math]b[/math]?
Which angle is corresponding to angle [math]h[/math]?
Which angle is corresponding to angle [math]f[/math]?
Which angle is corresponding to angle [math]a[/math]?
Consider the below diagram.
Which angle is corresponding to [math]a[/math]?
Which angle is corresponding to [math]c[/math]?
Which angle is corresponding to [math]b[/math]?
Which angle is[b] vertically opposite[/b] to [math]d[/math]?
Which angles are equal to [math]a[/math]?
Which angles are equal to [math]d[/math]?
Consider the below three diagrams.
Which of the above diagram shows angles which are equal to each other?