Geometry: An Interactive Journey to Mastery

A Return to Parallelism

Lesson 13

Topics
x Midpoint segments in triangles.
x Midpoint quadrilaterals within quadrilaterals.
x Transversals and triples of parallel lines.
x The median of a trapezoid.
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x corresponding angles: For a transversal crossing a pair of lines, two angles on the same side of the
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x median of a trapezoid: If a trapezoid has just one pair of parallel sides, then the line segment
connecting the midpoints of the two remaining sides is the median of the trapezoid.
x parallelogram: A quadrilateral with two pairs of parallel sides.
x trapezoid: A quadrilateral with at least one pair of parallel sides.
Results
x The line segment connecting midpoints of two sides of
a triangle is parallel to the third side of the triangle and
is half its length.
x If, for a triple of parallel lines, one transversal
segment is bisected by them, then so are all
WUDQVYHUVDOVHJPHQWVͼ௘6HHFigure 13.1௘ͽ
x The line that connects the midpoints of two transversal
segments to a pair of parallel lines is also parallel to
WKRVHOLQHVͼ௘6HHFigure 13.2௘ͽ

a

b

a = b

Figure 13.1

Figure 13.2