Analyze which lines form the angles. Then determine what those lines are called. Finally, use the appropriate theorem or postulate to find the relationship between the angles. Consider the transversal and parallel lines relationship.
Congruent, corresponding angles.
Practice makes perfect
We are given the following diagram and asked to find the relationship between angles ∠ 1 and ∠ 5.
In order to do so, we need to analyze the lines that form the angles and the positions of the angles.
If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent.
According to this postulate, we can conclude that ∠ 1 and ∠ 5 are congruent, which means that their measures are the same.
Extra
An Example of Corresponding Angles in a Game
In many games and sports, lines and angles are important but sometimes overlooked. Players who use these geometric principles can gain advantages. Here, two basketball players move straight towards the basketball hoop, parallel to one another. One player passes the ball, following the path of a transversal, to the other player.
Now, look at the basketball court with part of the diagram from the exercise displayed over it.
Playing with corresponding angles in mind, the two players are in an efficient position to take advantage of the court's dimensions. Imagine if their teammates were to position themselves at or near corresponding angles also!
