Download 7 bisect angles-bisect segment construction.notebook

#7 bisect angles­bisect segment construction.notebook
September 12, 2014
BISECT A SEGMENT
Warm Up #8
Points A, D, F, and X are on a segment in this order. AD = 15, AF = 22, and AX = 30. Find each length.
1. DF
0°
19
2. FX
B
Suppose B is between A and C. Use the Segment Addition Postulate to solve for x. Then find the lengths of AB and BC.
AB = 3x + 5
BC = 2x + 7
A
AC = 37
http://www.mathopenref.com/constbisectline.html
http://www.mathopenref.com/constcopyangle.html
BISECT A SEGMENT
Warm­up #9
STEPS:
1. Place your pointer at A, extend your compass so that the
distance exceeds half way. Create an arc.
Match the following with the correct notation and write a
definition for each.
2. Without changing your compass measurement, place your
point at B and create the same arc. The two arcs will
intersect. Label those points C and D.
3. Connect C and D using your straight edge. The intersection
of AB and CD is the bisector - label it M for midpoint.
1. ___ Point
A.
2. ___ Line
B.
3. ___ Segment
C.
4. ___ Ray
D.
5. ___ Circle
E.
Vocab
angle: two different rays that have the same initial point
A
sides BA and BC
9/12 - Angles and Angles Bisectors
(1.4/5)
vertex B
B
C
*Angle can be written as:
B,
ABC, CBA *
Angles with the same measure are called congruent angles.
Objective: To use angle postulates and bisect angles
ABC ≅
m ABC = m DEF
A
B
DEF
read as "measure of angle ABC"
40
C
D
E
40
F
congruent arcs
1
#7 bisect angles­bisect segment construction.notebook
September 12, 2014
Use the Angle Addition Postulate to find the measure of the
Angle Addition Postulate: If P is in the interior of RST, then
m RSP + m PST = m RST
unknown angle.
1.
2.
D
A
51
52
42
B
R
P
3.
47
S
m RSP = 60
D
m ABC = 103
(x+7)
(x­20)
23
B
m RST = ____
A
D
70
C
m ABD = _____
4.
A
T
m PST = 47
B
C
m ABC = ______
60
112
D
A
C
B
C
x = _____ m ABD = _____ m DBC = _____
m ABC = _____
angle bisector: a ray that divides an angle into 2 adjacent angles
that are congruent
adjacent angles: two angles are adjacent if they share a common
vertex and side, but have no common interior points
C
A
G
E
C
2.
R
R
m RPT = ____
EFG and HFI are NOT adjacent
adjacent
20
Examples
1.
I
ABC and CBD are
BD d
ivide
s (bis
2 con
ects) grue
nt ≅
( ) an ABC in
to gles If m ABD = 20 and m DBC = 20 , then the m ABC = 40 .
F
D
D
20
B
H
B
A
he an t me
arcs gles are
an
t (≅)
ruen
cong
T
T
m RPS = ____
19
P
39
P
3.
R
m TPS = ____
m RPS = ____
S
S
m RPT = ____
T
m TPS = ____
98
P
CLOSURE
Algebra Examples
BT bisects
1.
ABC. Find the value of x.
What is the difference between the angle addition
postulate and an angle bisector?
A
2.
A
S
T
B
T
B
HOMEWORK
C
3.
A
C
T
B
pg 29 20-28 (copy and measure each angle), pg 39
37-42
C
2