Two lines that are stretched into infinity and still never intersect are called coplanar lines and are said to be parallel lines. The symbol for “parallel to" is//.

If we have two lines (they don't have to be parallel) and have a third line that crosses them as in the figure below - the crossing line is called a transversal:

In the following figure:

If we draw to parallel lines and then draw a line transversal through them we will get eight different angles.

The eight angles will together form four pairs of corresponding angles. Angles F and B in the figure above constitutes one of the pairs. Corresponding angles are congruent if the two lines are parallel. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs.

Angles that are in the area between the parallel lines like angle H and C above are called interior angles whereas the angles that are on the outside of the two parallel lines like D and G are called exterior angles.

Angles that are on the opposite sides of the transversal are called alternate angles

e.g. H and B.

Angles that share the same vertex and have a common ray, like angles G and F or C and B in the figure above are called adjacent angles. As in this case where the adjacent angles are formed by two lines intersecting we will get two pairs of adjacent angles (G + F and H + E) that are both supplementary.

Two angles that are opposite each other as D and B in the figure above are called vertical angles.

Vertical angles are always congruent.

Two lines are perpendicular if they intersect in a right angle. The axes of a coordinate plane is an example of two perpendicular lines.

A F G D are exterior angles

B E H ZC are interior angles

B and E, H and C are consecutive interior angles

A and G, F and D are alternate exterior angles

E and C, H and B are alternate interior angles

A and E, C and G

D and H, F and B} are corresponding angles

Video lesson: Find the value of x in the following figure.

To see the solution look at the video in the next page.

Here we have two parallel lines and we’re given just this angle and we want to find this angle x. There are 2 important things we need to be able to do to find that angle, first of all since these are parallel, we can see that these are corresponding angles. So I’ll just note that by a similar arc and we’ll give these tick marks to say that they’re the same, in the same way that we say these are parallel. So this is 110 degrees as well, so that’s the first thing that we need to do. The second thing we need to do is to see that if this is a straight line then this total sum, 110 + x, is going to equal to 180. So 110° + x = 180° because the angle of a straight line is 180°. So then we can just solve for x from here. So x is just going to be 180 – 110, so x = 180 – 110 gives us x = 70°.