Geometry: An Interactive Journey to Mastery

Lesson 13: A Return to Parallelism

x The median of a trapezoid is parallel to the two parallel

sides of the trapezoid and has length the average of the

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Summary

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back to parallelism. In this lesson, we explore the consequences

of connecting midpoints in sides of triangles and quadrilaterals

and in segments of transversals for parallel lines.

Example 1

Provide the full details that explain why, in Figure 13.4,

length a matches length b.

Solution

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mark the lengths p and q.

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Because the scale factor is 2, p + q = 2p, giving p = q.

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factor 2, because p = q. Consequently, a + b = 2b,

giving a = b.

Example 2

Provide the full details that explain why, in Figure 13.6,

the central line is parallel to the two given parallel lines.

Solution

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shown in Figure 13.7.

b

a

x

x=ab+ 2

Figure 13.3

a

b

Figure 13.4

q a

p b

Figure 13.5

Figure 13.6

PQ

Figure 13.7