Download Chapter 1-4 Angles and Segments

Chapter 1-4 Angles and
Segments
To Use and apply the Segment
Addition Postulate and Angle
Addition Postulate


To classify angles
1.4 Congruent Segments and
Congruent Angles
If 2 segments are ≅, they are =
in length.
If 2 angles are ≅, they are
equal in size.
Measuring & comparing
segments
-9
-7
-2
0
2
3
6
9
A
B
C
D
E F
G
H
Compare
1. AB ___ EF
3. CD ___DE
2. BC____EG
A
B
C
Segment Addition Postulate
AB + BC = AC
i.e. the parts = the whole
M
A
N
1. If MA = 12 and AN = 11,
then MN =______
2. If MN = 38 and AN = 22,
then MA = ______
AC = 38
Find x, AB,& BC.
B
A
2X + 5
C
3X - 2
N
M
O
-12
MN = 8
MO=21
Find the coordinates
of N and O.
NO = _____
Midpoint of a segment
A point that divides a segment into 2
congruent parts.
Segment Bisector
A line, line segment, ray or
plane that intersects a
segment at its midpoint
How many midpoints can a segment
have?
How many segment bisectors can a
segment have?
A
M
There are an infinite number of segment
bisectors.
B
5a - 16
2a + 5
H
O
Find a, HO, and OT.
T
M
-26
R
P
-2
If R is the midpt of MP find
MR=_____
RP=_____
and the coordinate of R.
R
-10
4x
M
3x
P
18
Find x and AB, BC and AC.
What are the coordinates of
B if C’s coordinate is 70?
6X - 8
A
2X + 20
B
C
W
X
Y
Z
T
R
-14
-8
-2
0
4
9
Find the possible coordinates of M if YM = 5.
Find the possible coordinates of E on YR if
YE = 9

Assignments
1st Part of section1.4
Assign pp. 29-31
(1-15 all, 29-35 all)
Part II
Angles

What is an angle? How do you
name the following angle?
A
Angle - the union of 2 noncollinear
rays whose intersection is a point
called the vertex.
<ABC or <CBA or <B
B
C
When naming an angle
remember…….



The vertex point must always be in the
middle
A point from each ray should be on
either side of the vertex point
You can name an angle with the vertex
pt if it is the only angle at the vertex
Given < ABC
Vertex is B
 Ray BA
 Ray BC


Can be named <CBA or
<B
Classify Angles




Acute angles- angles less than 90
degrees
Right angles- angles whose measure
= 90 degrees
Obtuse angles- angles greater than
90 degrees
Straight angles- angles = 180
degrees (a straight line)
Draw an example of each type
of angle.
1.
2.
3.
4.
Complementary Angles
2 angles whose sum
is 90
H
1
2
O
W
Supplementary Angles
Two angles whose
sum is 180.
B
H
60
120
E
Y
T
A
Adjacent Angles
Two angles that have a common ray, a
common vertex, and no common interior
points.
H
1
E
P
2
L
Linear Pair
Two angles that are adjacent
and supplementary.
D
1
A
2
B
C
Angle Addition Postulate
m < 1 + m < 2 = m <TAP
T
E
1
A
2
P
Find x and the measure of
the 2 angles.
Definition of
Linear Pair
2x + 8
6 x - 84
Find x and each angle.
Explain your answer.
4x
2x + 18
Definition of
complementary
angles.
1
A
2
E
3
D
m<1=m<3
m < 1 = 10 less than twice
m<2
Find x and the measure
of each angle.
m < AOB = 4x + 3, m < BOC = 7X, m <
AOD = 16X -1
Solve for x and find the angle measures.
Assignments
2nd part of 1.4
Pgs 30-33
(16-19,27-28,70-72,75-78)
Notebook Quiz
1. Write an equation for the
following.
2x + 8
6 x - 84
2. Write an equation
for the following:
R
-10
4x
M
3x
P
18
Draw a picture to demonstrate
each of the following:
3. Complementary Angles
4. Linear Pair
Notebook Quiz
1. Write an equation for the
following.
2x + 8
6 x - 84
2. Write an equation
for the following:
R
-10
4x
M
3x
P
18
Draw a picture to demonstrate
each of the following:
3. Complementary Angles
4. Linear Pair