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Segment Partitions

For your notebook, be sure to include the vocabulary for this section and the Midpoint Formula.

[(x sub 1 + x sub 2)/2,(y sub 1 + y sub 2)/2 ]

Vocabulary

  • congruent
  • ratio
  • midpoint
  • supplementary
  • segment
  • bisector

given points (x1, y1) and (x2, y2).

Segment Partitions

From the previous lesson we know a line segment can be divided into smaller line segments. The whole is simply the sum of its parts.

AB + BC+ AC
6 inc + 3 in = 9 in

line segment with point A on right end, 6 inches to point B and 3 more inches to point C on left end

A point can partition the segment in a given ratio. A ratio is a fraction that describes the relationship between two numbers such as the segment partitions. Example: The ratio between AB and BC is

AB/BC = 6/3 = 2/1 or 2

State the ratio of the two line segment partitions.

line segments with point A on the right end, 2 inches to point B, 10 inches to point C on the left end

AB/BC = ?/? = ?/?
Answer: AB/BC = 2/10 = 1/5

Congruent Segments

Sometimes a point partitions a segment with a ratio 1/1. When this happens partitions have equal length measurement which means the segments are congruent. The symbol for congruent is:

equal sign with wave line over
AC congruent to CB
line segments with point A on the right end, 4 inches to point C, 4 inches to point B on the left end

Midpoint

The midpoint of a segment is the point that divides the segment into two congruent segments. Matching tic marks identify congruent segments in diagrams.

line segment with point A on right end, point B on left end, point C at the midpoint, tic marks in each congruent segment

Think of the relationships between the segments AC congruent to CB. If AC = 12, then CB = 12. Also, line segment AB is twice the measure of segment AC or segment CB; so if CB = 7 then AC =7 and AB = 2 x CB.

Open Apply the Definition of a Midpoint to Find Unknown Values and Segmented Lengths in a new tab

Segment Bisector

A segment bisector is a segment, ray, line, or plane that intersects a segment at its midpoint.

two line segments intersecting at the midpoints; one line has points A and B at each end, the other has points E and D at each end

Indicating Congruence

If there are multiple pairs of congruent segments (which are not congruent to each other) in the same figure, use two tic marks for the second set of congruent segments, three for the third set, and so on. Notice the marks on the following parallelogram.

four line segement; two each are parallel

Finding Midpoint

When graphing on a coordinate plane you can find the midpoint of a line segment if you know the coordinates of the endpoints. This method is summarized as the midpoint formula.

[(x sub 1 + x sub 2)/2,(y sub 1 + y sub 2)/2 ]

Open Apply the Midpoint Formula to Find the Midpoint of a Segment Given the Coordinates of Its Endpoints in a new tab