chapter 1-4 angles and segments
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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. - PowerPoint PPT PresentationTRANSCRIPT
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.
A B C D E F G H
-9 -7 -2 0 2 3 6 9
Measuring & comparing segments
Compare
1. AB ___ EF 2. BC____EG
3. CD ___DE
Segment Addition Postulate
A B C
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 = ______
A B C2X + 5 3X - 2
AC = 38Find x, AB,& BC.
MN = 8 MO=21Find the coordinatesof N and O.NO = _____
M N O-12
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 B
There are an infinite number of segment bisectors.
H O T
2a + 5 5a - 16
Find a, HO, and OT.
M R P-26 -2
If R is the midpt of MP findMR=_____ RP=_____and the coordinate of R.
R M P-10 18
4x 3x
A B C
6X - 8 2X + 20
Find x and AB, BC and AC.
What are the coordinates of B if C’s coordinate is 70?
-14 -8 -2 0 4 9
W X Y Z T R
Find the possible coordinates of M if YM = 5.
Find the possible coordinates of E on YR if YE = 9
Assignments1st 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
B C
Angle - the union of 2 noncollinear rays whose intersection is a point called the vertex.<ABC or <CBA or
<B
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
12
H
O W
Supplementary Angles
Two angles whose sum is 180.
120 60
H
E Y T A
B
Adjacent Angles
Two angles that have a common ray, a common vertex, and no common
interior points.
12
H
E L
P
Linear PairTwo angles that are
adjacent and supplementary.
A B C
D
1 2
T
A P
E
1 2
Angle Addition Postulate
m < 1 + m < 2 = m <TAP
2x + 8 6 x - 84
Find x and the measure of the 2 angles.
Definition of Linear Pair
2x + 184x
Find x and each angle.
Explain your answer.
Definition of complementary angles.
12 3
A E D
m < 1 = m < 3m < 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 1.4Pgs 30-33 (16-19,27-28,70-72,75-78)
2x + 8 6 x - 84
Notebook Quiz
1. Write an equation for the following.
R M P-10 18
4x 3x
2. Write an equation for the following:
Draw a picture to demonstrate each of the
following:
3. Complementary Angles
4. Linear Pair
2x + 8 6 x - 84
Notebook Quiz
1. Write an equation for the following.
R M P-10 18
4x 3x
2. Write an equation for the following:
Draw a picture to demonstrate each of the
following:
3. Complementary Angles
4. Linear Pair