Vertical and corresponding angles

From true

In class, we measured the angles created by one line crossing two parallel lines as in the figure below.

[edit] Vertical Angles

Vertical angles occur whenever two lines cross. They are the angles across from each other -- across the vertex. Looking just at lines AC and GH, which meet at point B, there are two pairs of vertical angles formed.

Angle ABG = Angle CBH

Angle ABH = Angle CBG

Can you come up with a proof that vertical angles are equal? Hint: You can use addition and subtraction and the idea of a "straight angle" (a line).

[edit] Corresponding Angles

When a line crosses two (or more) parallel lines, the same sets of angles are formed at each intersection.

Angle ABH corresponds to Angle DEH

Angle ABG corresponds to Angle DEG

Angle CBH corresponds to Angle FEH

Angle CBG corresponds to Angle FEG

The angles which correspond to each other equal each other. Can you prove it?

[edit] Alternating Interior and Exterior Angles

Once you know that vertical and corresponding angles are equal, it is easy to find other sets of equal angles.

In between the two parallel lines (in the interior) and on either side of the transversal (the line that crosses the parallel lines) are the alternate interior angles.

Angle DEH = Angle CBG

Angle ABG = Angle FEH

Outside the two parallel lines (on the exterior) and on either side of the transversal are the alternate exterior angles.

Angle DEG = Angle CBH

Angle ABH = Angle FEG