section 1-2
Measuring and Constructing Segments
coordinate - the number on a number line that is paired with a particular point
number line
B
A
C
E
D
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
distance = absolute value of the difference of the coordinates of two points
length of a segment - the distance between the endpoints of the segment
problem # 1 - Find each length on the number line above:
a. DE
b. AC
congruent segments - segments that have the same length
* Tick marks are used in a diagram to indicate that segments have the same length.
C
D
B
A
E
F
AB = FE and BC = ED
equal length segments vs. congruent segments
A
B
5 inches
AB
C
D
5 inches
CD or AB
CD
equal refers to the length of the segments, whereas congruent refers
to the actual physical segments
Geometric construction - a drawing that uses nothing more than a
compass and a straightedge
Constructing a Congruent Segment
Problem: Construct a segment congruent to AB.
B
A
Step 1: Draw a line k, choose a point on the line, and label it C.
k
C
Step 2: Open the compass to distance AB.
B
A
Step 3: Place the compass point at C and swing an arc through line k.
Label the intersection of the arc and line k as point D.
CD
AB
k
C
D
problem # 1 - Draw a line segment on your paper and use the construction
above to construct a congruent segment.
In order to say that a point B is between two points A and C, all three of the points
must lie on the same line, and AB + BC = AC.
problem # 2 - Point B is between points A and C; AC = 14 and BC = 11. Find AB.
problem # 3 - Point S is between points R and T. Find RT.
R
S
2x + 7
T
28
4x
midpoint of a segment - the point that bisects, or divides the segment into two
congruent parts.
problem # 4 - Point Q is the midpoint of PR. Find the value of x.
P
Q
3x - 4
R
x + 12
segment bisector - a ray, segment, or line that intersects a segment at its midpoint.
problem # 5 - Line m is bisects EF. Find the value of x.
5x
3x + 4
F
E
m