Transcript Measure / Classify

Section 1.4
 Measuring Segments
and Angles
Goal: After today, you will be able to:
Explain the Ruler Postulate and the
Segment Addition Postulate.
Use the Ruler Postulate and the Segment
Addition Postulate find the lengths of
segments.
Use the midpoint and some algebra
skills to find the lengths of segments.
Coordinates
Definition: A coordinate is a point’s
distance and direction from
zero on a number line.
Note the Notation for “length”
3
Postulates
Postulate 1-5 The Ruler Postulate: The points of a
line can be put into one-to-one correspondence with
the real numbers so that the distance between any two
points is the absolute value of the difference of the
corresponding numbers.
|
|
PK = 3 - -2 = 5
(distance is always positive)
Congruent Segments
Congruent segments are
Definition:
segments with the same
length.
Congruent segments can be marked with . . .
REMEMBER THIS POINT:
Numbers are equal to each other.
Shapes and figures are not equal to each other.
But if their MEASURES are equal, then they are
congruent.
Correct notation:
Incorrect notation:
Segment versus length - notation
6
Midpoint
Definition: a point that divides a segment into two
congruent segments
We also say that E bisects the segment.
“Between”
Definition: X is between A and B if AX + XB = AB.
AX + XB = AB
So, X is between
Points A and B
AX + XB > AB
Since not = ; we can conclude
That X is NOT ‘between’ points
A and B
Segment Addition Postulate!
(is something you already know how to use)
home
school
movies
Philly
The Segment Addition Postulate:
If three points A, B, and C are collinear and C is
between A and B, then: AC + CB = AB
Example: If AC = x , CB = 2x and AB = 12, then
Find x, AC and CB.
AC + CB = AC
x + 2x = 12
3x = 12
x=4
Final Answer:
x = 4
AC = 4
CB = 8
2x
x
12
Classwork Time.
Page 29-30 #’s 1-15 Odd.
Read pages 27-29
Try #’s 18, 20-23, 27
11
Section 1.4b - Angles
12
Measuring Angles
Goals:
1. Define terms used in relation
to angles.
2. Name angles in several ways.
3. Measure and classify angles.
4. Identify congruent angles.
5. Recognize special pairs of
angles.
13
Angle Terms
- An angle is formed by two rays
with a common endpoint.
- The rays are called the sides.
- The common endpoint where the
sides meet is called the vertex.
- The angle measure is measured
in “degrees”. Ex: 55º
14
Naming Angles
A
1
C
B
Or Geek
Letters!
 - Theta
- Alpha
 - Beta
Measuring Angles
16
Classifying Angles
An acute angle has a measure that is
greater than 0 degrees but less than 90
degrees.
A right angle has a measure of exactly 90
degrees.
An obtuse angle has a measure greater than
90 degrees but less than 180 degrees.
A straight angle has a measure of exactly
180 degrees.
Congruent angles are angles that have the same
measure.
17
Measure and Classify
C
A
m<ABC =
B
Classify <ABC:
18
Measure and Classify
A
C
m<ABC =
B
Classify <ABC:
19
Measure and Classify

Measure

/
Classify
=
=
20
21
Postulate 1-8: The Angle Addition
Postulate
22
Using the Angle Addition Postulate
23
Special Pairs of Angles
two angles
whose sides are
opposite rays
Vertical Angles
are Congruent!!
two coplanar angles
with a common side, a
common vertex, and no
common interior points
(they don’t overlap)
24
Special Pairs of Angles
two angles whose
measures have a sum of
90 degrees.
two angles whose
measure have a sum of
180 degrees.
Each angle is called the
complement of the other.
Each angle is called the
supplement of the other.
25
Classwork
Page 30, #16, 18,
20-23, 27, 29-32,
42-49
26