Geometry: An Interactive Journey to Mastery

We do not know if PQ is parallel to the pair of lines.
Imagine drawing a line through P that is in fact parallel to the pair of lines. By Example 1, this line meets the
VHFRQGWUDQVYHUVDOVHJPHQWDWLWVPLGSRLQW²QDPHO\Q. Thus, PQ is the parallel line through P, and therefore,
PQ is indeed parallel.
Example 3
Find the values of x and y in Figure 13.8.
Solution
The unlabeled angle in the small triangle has measure 59°.
Because the line connecting midpoints in a triangle is parallel to the base of the triangle, this angle and y are
congruent corresponding angles. Consequently, y = 59°.
Also, x = 8, because the line connecting midpoints in a triangle is half the length of the base of the triangle.
Study Tip
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lines are parallel.
Pitfall
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matter of author’s taste and, therefore, vary from author to author.

1. Given: M is midpoint of AB.
   MQ BC||.
   Prove: Q is midpoint of AC.
   ͼ௘6HHFigure 13.9௘ͽ

20° 101°

(^55)

4

y

x

Figure 13.8

Problems

A

Q

B C

M

Figure 13.9