NAME
DATE
5-1
PERIOD
Practice 5-1 and 5-2
Perpendicular Bisector A perpendicular bisector is a line, segment, or ray that is
Perpendicular Bisector
Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant
from the endpoints of the segment.
Converse of Perpendicular
Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the
perpendicular bisector of the segment.
Example 1
𝑩𝑫 is the perpendicular
bisector of 𝑨𝑪. Find x.
Find the measure of 𝑭𝑴.
Example 2
F
C
5x – 6
2.8
B
G
K
D 3x + 8
A
M
Exercises
Find each measure.
1. XW
2. BF
A 4.2 B F
Y
5
7.5
Z
5
19
W
19
X
E
Median of a triangle - ____________________________________________________________________
3. Draw scalene 𝛥ABC with median 𝐴𝑀.
Chapter 5
4. Draw isosceles 𝛥XYZ with vertex Z and median 𝑀𝑍.
5
Glencoe Geometry
Lesson 5-1
perpendicular to the given segment and passes through its midpoint. Some theorems deal
with perpendicular bisectors.
NAME
DATE
5-1
PERIOD
Practice 5-1 and 5-2
5. a. Graph 𝛥ABC at the right where A(-5,1), B(1,2, and C(-3, 3).
b. Find the coordinates of median 𝐵𝑀 of 𝛥ABC.
c. Write the equation of the line that contains median 𝑀𝐵.
Example
Altitude of a triangle - _____________________________________________________________________
6. Draw scalene 𝛥ABC with altitude 𝐵𝐷.
7. Draw isosceles 𝛥XYZ with vertex Y and altitude 𝑌𝐷.
If a triangle is an isosceles triangle, then the median and altitude (from the vertex) are the same segment.
Find the altitude of the following triangles (from the vertex).
B
13
A
Chapter 5
8
10
P
Y
C
X
8
6
6
14
Z
Q
14
14
Glencoe Geometry
R
Find the area of the following triangles. A = bh.
Z
L
16
Y
20
20
24
16
M
X
5. a. Graph 𝛥ABC at the right where A(-2, 4), B(4,4), and C(1,-2).
b. Write the equation of the line that contains altitude 𝐷𝐵.
5. a. Graph 𝛥ABC at the right where A(-2, 4), B(4,4), and C(1,-2).
b. Write the equation of the line that contains altitude 𝐴𝑋.
20
M