MEASURING
SEGMENTS
AND
ANGLES
Assignment
Page 29 - 30
2 – 30 even
31, 32, 34, 36, 42, 44, 46,
70, 72, 76, 78
Ruler Postulate 1- 5
The distance between any two points is the
absolute value of the difference of the
corresponding numbers
Example:
Length of AB is
a–b
which in this
Case would be 2 – 5
Or the - 3 which is 3
B
A
Congruent segments
segments of the same length
A
AB = CD
B
C
or
D
AB = CD
The two tick marks is a way of showing
that the two segments are congruent
A
B
C
D
Compare CD and DE
CD =
-2 – 0 =
DE =
0–2 = -2
CD = DE
-2 = 2
= 2
E
Segment Addition Postulate 1- 6
If three points A, B, and C are collinear and B is
between A and C, then AB + BC = AC
Example :
From previous CD = 2 and DE = 2
CE = -2 -2 = -4 = 4
A
B
C
D
E
2+2=4
4x – 20
E
2x + 30
F
G
EG = 100. Find the value of x, then EF and FG
EF +
FG
= EG
(4x – 20 ) + ( 2x + 30 ) = 100
6x + 10 = 100
6x = 90
x = 15
EF = 4x – 20 = 4(15) – 20 = 40
FG = 2x + 30 = 2(15)+ 30 = 60
3x +1
E
EG = 64
2x-2
F
Find EF and FG
G
AB = 5x + 3 and BC = 7x – 9 Find AC
A
B
C
Midpoint of a Segment
point that divides the segment into two
congruent segments
We are bisecting the segment
A
B
AB = BC
C
Using midpoint
5x + 3
7x – 9
P
T
T is midpoint, find PT, TQ and PQ
PT = TQ
definition of midpoint
5x + 3 = 7x – 9
substitution
5x + 12 = 7x
add 9 to each side
12 = 2x
6= x
subtract 5x from each side
divide each side by 2
PT = 5x + 3 = 5(6) + 3 = 33
TQ = 7x – 9 = 7(6) – 9 = 33
PQ = 66
Q
Angles
two rays with the same endpoint
rays are the sides of the angle
the endpoint is the vertex
vertex
rays
A
Naming angles
D
1
2
B
<1
Use the number
C
<ADB
<BDA
Name the two sides with the vertex in the middle
If we were referring to <ADC we could also say that
this was <D
Measuring Angles
Use a Protractor
Classify Angles
according to their measurement
acute
less than 90 degrees
0 < x < 90
x
Right angle
exactly 900
x = 90
Obtuse angle
greater than 900
but less than 1800
90 < x < 180
Straight angle
two opposite rays
1800
Angle Addition Postulate
If point B is in the interior of < AOC, the
m<AOB + m<BOC = m <AOC
In other words, if you
B
A
have two small
adjacent angle they
C
will add up to the
0
larger angle
If < AOC is a straight angle, the m<AOB +
m<BOC = 180
B
A
O
C
Try this!
If m<DEG = 145, find the m<GEF
G
D
E
145 + x = 180
x = 35
m< GEF = 350
F
Congruent Angles
Angles that has the same measure
These angles can be marked to show they
are congruent