To find: The correct values to complete the given table.
Answer to Problem 17WE
AR | RT | AT | AN | NP | AP | RN | TP |
8 | 8 | 16 | 6 | 6 | 12 | ? | ? |
Explanation of Solution
Given information:
AR | RT | AT | AN | NP | AP | RN | TP |
? | 8 | 16 | 6 | ? | ? | ? | ? |
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 AR,
The point R lies on the line AT, as shown in the given figure. The value of AR will be the sum of
Therefore,
For NP,
As the line RN is parallel to the line TP, therefore,
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,
As there are no values for the parallel lines therefore, it is impossible to find out all other variables.
Hence, the new table will be shown as;
AR | RT | AT | AN | NP | AP | RN | TP |
8 | 8 | 16 | 6 | 6 | 12 | ? | ? |
Chapter 7 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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