Exercise 34 Page 394

The two postulates can be useful in different ways to get information from the bar graph.

Ruler Postulate

The Ruler Postulate is used to measure the length of a segment. In this case, we can use it to calculate the number of wins or loses during a year. For example, if we want to know the number of wins during year $1,$ we should measure the length of the first green bar.

The first step of the Ruler Postulate is now to match the points with some coordinates.

From the picture above, we can estimate the coordinates to be $0$ and $6.$ The next step of the Ruler Postulate is to take the absolute value of the difference between the points. Therefore, the number of wins during year $1$ is $6.$

Segment Addition Postulate

If we have three points on a straight line, we can use the Segment Addition Postulate to calculate the total length. If know the total length and one piece of the segment, then we can calculate the second piece's length. In this case, we could use the Segment Addition Postulate to calculate the number of losses during year $1.$

The total number of wins and losses is $11,$ as shown in the picture above. From calculations with the Ruler Postulate, we know that there were $6$ wins. The Segment Addition Postulate tells us that the sum of the wins and losses equals the total number of games played. Since we know the wins and the total number of games, we can calculate the losses. Therefore, the team lost $5$ games during year $1.$