
To find: The correct values to complete the given table.

Answer to Problem 15WE
AR | RT | AT | AN | NP | AP | RN | TP |
12 | 8 | 20 | 18 | 12 | 30 | 15 | 25 |
Explanation of Solution
Given information:
AR | RT | AT | AN | NP | AP | RN | TP |
12 | ? | 20 | ? | ? | 30 | 15 | ? |
Proportional lengths: Point L and M lie on AB and CD, respectively. If NA, then AB and CD are divided proportionally.
If ΔRST : PQ || RS
Then, NA
Now consider a triangle ATP, in which a line intersects AT and AP, the sides of the triangle, at the points R and N on the AT and AP respectively.
Thus,
AR | RT | AT | AN | NP | AP | RN | TP |
12 | ? | 20 | ? | ? | 30 | 15 | ? |
For RT,
The point R lies on the line AT, as shown in the given figure. The value of RT will be the sum of AT−AR.
Therefore,
For AN,
As the line RN is parallel to the line TP, therefore,
For NP,
The point N lies on the line AP, as shown in the given figure. The value of NP will be the sum of AP−AN.
Therefore,
For TP,
Use the proportion,
Hence, the new table will be shown as;
AR | RT | AT | AN | NP | AP | RN | TP |
12 | 8 | 20 | 18 | 12 | 30 | 15 | 25 |
Chapter 7 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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