Transcript Slide 1

We’re going to do two
sections today.
1.3 - Measuring segments
1.4 – Measuring angles
Please begin on the warm up.
Thanks
Let’s grade your homework
1.3
Measuring Length
How do you measure distance on a
number line?
-3
-2
-1
0
1
2
3
What is the distance between -2 and 3
4
5
5
What is the distance between -2 and -7
5
What is the distance between 5 and 17
12
What is the distance between 0 and -5
5
What is the distance between 10 and -3
13
Notice that all the DISTANCES ARE POSITIVE!
6
7
What
mathematical
operation
makes all
answers
positive?
ABSOLUTE VALUE!!!
Measuring length
a
b
♥ On a number line, the distance between
the coordinates a and b is |a-b| or |b-a|.
♥ This will give you the measure of the
segment.
WRITE THIS DOWN
Notation for MEASURE of a
segment
mXY or XY
If you use the bar, use the m.
If you don’t use the bar, don’t use the m
In this notation, we are talking about the LENGTH of the
segment NOT the segment itself.
X
-3
Y
-2
mXY = |-3 - 0|
-1
0
Z
1
2
3
XZ = |-3 - 4|
= |-3|
= |-7|
= 3
= 7
4
5
6
7
CONGRUENT
• Means the same size and same shape
~
• The congruent symbol is =
A
A
B
B
E
C
D
C
D
~
AB = CD
Segment Congruence Postulate
♥ If two segments are
congruent, then they have the
same measure.
Important notation
If AC
A
~
=
BD then AC = BD
B
E
C
This says: if the segments are
CONGRUENT
then the measures are EQUAL.
D
Without the bar
means NUMBER
AC is a NUMBER
AC is NOT
Segment Addition Postulate
P
R
Q
If point R is between points P and Q, then PR + RQ = PQ
A
B
3
AB + BC = AC
3 + 5 = AC
8 = AC
A
C
B
x
5
C
3x + 1
AC = 25
X + 3x + 1 = 25
4x + 1 = 25
4x = 24
X=6
Find the measure of
each segment and
CHECK YOUR
ANSWER
1.4 Measuring Angles
Angle Addition Postulate
m< PQS + m< SQR = m< PQR
S
P
Q
R
Which one makes sense?
< A + < B = 85°
Or
A
B
m < A + m < B = 85°
Angle Congruence Postulate
♥ If two angles have the same measure,
then they are congruent.
Angles
• Acute Angle – An angle whose measure is less than 90°.
• Right Angle – An angle whose measure is exactly 90°.
• Obtuse Angle – An angle whose measure is greater than
90° and less than 180°.
• Straight Angle - An angle whose measure is exactly
180°.
• Reflex Angle – An angle whose measure is greater than
180° and less than 360°.
• COMPLEMENTARY Angles – Exactly two angles whose
sum is 90°. Each angle is a COMPLEMENT of the
other.
• SUPPLEMENTARY Angles = Exactly two angles whose
measure is 180°. Each angle is a SUPPLEMENT of the
other.
30°
A
60°
B
120°
C
Complementary angles are < A and < B
< A and < B are complements of each other
< A and < C are supplementary angles
< A and < C are supplements of each other
Are you
doing
ok?
Linear Pair Property
If two angles form a line, they are a linear
pair AND are supplementary.
125°
55°
Your assignment
1.3 – pgs 25-27;
17-47 odds
1.4 – pgs 33-35;
11-39 odds