Download Midsegments of Triangles

Measuring Segments
Geometry
Date
Name
Length of a Line Segment - The absolute value of the difference of the endpoints
coordinates.
| __ _ – _ __ |
-2
0a 2
4
b6
8
The length of a line segment is expressed by writing the line segment without the bar.
Length of AB is expressed as
When numerical expressions have the same value, we say they are equal (=).
Similarly, if two segments have the same length, then the segments are congruent (  ).
A
1 in.
B
A
B
D
1 in.
E
D
E
______  ______
______ = ______
Segment Addition Postulate ______ + ______ = ______
A
B
C
Midpoint of a Segment - A midpoint divides a segment into two congruent segments.
B is the midpoint of AC .
A
B
______ = ______
C
______  ______
______ =
1
______
2
______ 
1
______
2
______ =
1
______
2
______ 
1
______
2
Segment Bisector - A segment bisector divides a segment into two congruent segments.
DBE bisects AC .
A
B
______ = ______
D
______  ______
C
E
Perpendicular Bisector - A segment bisector that is also perpendicular to the segment at
its midpoint.
DBE is the perpendicular bisector of AC . ______ = ______
______  ______
D
DBA , DBC , EBA , EBC are right angles.
A
B
E
C
1. Find the length AB .
A
-2
B
0
2
4
6
8
2. Find LM if L is between N and M, NL = 6x – 5, LM = 2x + 3, and NM = 30. Justify
and explain each step.
N
L
M
3. If B is between A and C, AB = 20, BC = 4x, and AC = 7x + 2, find the value of x.
Justify and explain each step.
4. If Y is the midpoint of XZ , XY = 2a + 11 and YZ = 4a – 5, find the value of a and XZ.
Justify and explain each step.
5. If Y is the midpoint of XZ , XZ = 30 and YZ = 3x, find the value of x. Justify and
explain each step.
Reflection:
1. In the diagram, JL = 120. What are JK and KL?
2. U is the midpoint TV . What are TU, UV, and TV.