5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
11/8/16 - Warm Up Problem
Find the measure of each numbered angle.
3
2
55
1
55
o
o
4
135
o
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Section 5.2+5.4 - Bisectors, Medians, and Altitudes
Goals:identify angle bisectors, perpendicular bisectors, medians, and
altitudes and use their properties to find measures
Perpendicular Bisector: a segment or line that makes a
o
90 with another segment and goes through the midpoint
CD is a perpendicular bisector of AB.
C
What is true about ΔACD and ΔBCD?
A
D
B
What must be true about AC and CB?
Why?
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Theorem 5.2 - Perpendicular Bisector Theorem
If a point is on a perpendicular bisector of a segment,
then it is equidistant from the endpoints of the segment.
What is the most precise name for segment GJ?
G
2x ­ 5
F
13
J
H
Find the value of x.
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Angle Bisector: a ray that cuts an angle into two
congruent angles
80
90
100
70
110
60
110
50
100
90
120
40
150
70
130
60
130
140
30
120
80
140
50
0°
40
150
30
20
160
160
10
0
20
170
10
180
0
170
180
50°
25°
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Theorem 5.4 - Angle Bisector Theorem
If a point is on the bisector of an angle, then it is
equidistant from the two sides of the angle.
If AD is an angle bisector,
then CD = DB.
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Medians and Altitudes
Median: segment starting at a vertex and going
to the middle of the opposite side
Altitude:
segment starting a vertex and making a
90 degree angle with the opposite side
(it is like the height of the triangle)
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Identify each as a perpendicular bisector, angle bisector, median, or altitude.
Do these in your notes.
5.2­5.4 bisectors, medians, and alt..notebook
Assignment:
5.2-5.4 Worksheet
(front side only)
November 08, 2016
5.2­5.4 bisectors, medians, and alt..notebook
11/9/16 - Warm Up Problem
November 08, 2016
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
5.2­5.4 bisectors, medians, and alt..notebook
Points of Concurrency
Point of Concurrency: a point where three or more
lines all intersect
Circumcenter: the point where the perpendicular
bisectors of a triangle intersect
Properties of the Circumcenter
1) It is equidistant
from the 3 vertices
2) It is the center of
the circle circumscribed
around the triangle
November 08, 2016
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Incenter: the point where the
angle bisectors of a triangle
intersect
Properties of the Incenter
1) It is equidistant from
the 3 sides of the triangle
2) It is the center of the
circle inscribed inside the
triangle
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Centroid: the point where the
medians of a triangle intersect
Properties of the Centroid
1) It is the center of gravity
of the triangle
2) It is located exactly
two-thirds of the way from
the vertex to the midpoint
5.2­5.4 bisectors, medians, and alt..notebook
November 08, 2016
Orthocenter: the point where the
altitudes of a triangle intersect
5.2­5.4 bisectors, medians, and alt..notebook
Assignment:
5.2-5.4 Worksheet
(back)
November 08, 2016