To find: The correct values to complete the given table.
Answer to Problem 16WE
AR | RT | AT | AN | NP | AP | RN | TP |
9 | 18 | 27 | 13 | 26 | 39 | 12 | 36 |
Explanation of Solution
Given information:
AR | RT | AT | AN | NP | AP | RN | TP |
? | 18 | ? | ? | 26 | ? | 12 | 36 |
Proportional lengths: Point
Triangle Proportionality Theorem: if a line parallel to one side of a triangle intersects the other two sides, then it divided those sides proportionally.
If
Then,
Now consider a triangle
points
Thus,
For AN,
Use the proportion,
For AP,
The point N lies on the line AP, as shown in the given figure. The value of AP will be the sum of
Therefore,
For
As the line
For
The point
Therefore,
Hence, the new table will be shown as;
AR | RT | AT | AN | NP | AP | RN | TP |
9 | 18 | 27 | 13 | 26 | 39 | 12 | 36 |
Chapter 7 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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