Using a Ruler
• Length of segment:
Looking at the ruler…how long is segment CD?
CD a b Length of
3 units
**length is always the positive value of the
distance between the points
Ruler Postulate
•Postulate 1-5: Ruler Postulate
Distance between 2 points is the absolute value of their difference.
Congruent Segments
2 cm
2 cm
A B
DC
AB CD
C D
BA
AB CD
congruent segments—segments with the same length
**lengths **congruency
Ex 1: Use diagram to answer questions
a) Find the length of segment XZ 7
b) Find the length of segment XY 4
c) Find the length of segment YZ 3
d) Name 2 pairs of congruent segments
;XY ZW XZ YW
Segment Postulate
• Postulate 1-6: Segment Addition Postulate
If 3 points A, B, and C are collinear where B is between A and C, then
AB BC AC A
C
B
Ex 2: Solve for the missing variable
a)NA B
2 6x 7x25AB
2 6 7 25x x
3 1 25x
3 24x
8x
Find length of segment
AN and segment NB
10AN
15NB
Ex 2: Solve for the missing variable
b)D TS
2 8x 3 12x 60DT
2 8 3 12 60
5 20 60
5 80
16
x x
x
x
x
Find length of segment
DS and segment ST
24
36
DS
ST
Midpoint
• midpoint of a segment—the point that divides the segment into 2 congruent segments (middle point).
BA C
AB BC
Ex 3: Solve for the variable and segment lengths
a) M is the midpoint of segment RT.
Find segment lengths RM, MT, RT, and x.
MR T
5 9x 8 36x
5 9 8 36x x 45 3x
15 x
84
84
168
RM
MT
RT
Ex 3: Solve for the variable and segment lengths
b) Y is the midpoint of segment XZ and XZ = 28.
Find length of XY.
28
YX Z
14XY
Angles
• angle—formed by 2 rays with the same endpoint
1
B
A
C
vertex
side
side
Name an angle—trace angle
making sure vertex is in center
ABC
CBA
1
B
Ex 1: Naming angles
Name all the angles in the diagram
1, 2
, ,
, ,
JEN NES JES
NEJ SEN SEJ
21
E
J
N
S
Types of Angles
Acute Angle
Less than 90°
0 90x
x
Right Angle
90°
Obtuse Angle
Greater than 90°
90 180x
x
Straight Angle
x
x
180°
Angle Addition Postulate
Pretend we measured the following angles and found
these measures…
B
A
C
D
4060
What is the measure of
angle ABD?
100m ABD
Angle Addition Postulate
• Postulate 1-8: Angle Addition Postulate
1) If point B is in the interior of angle AOC, then…
m AOB m BOC m AOC
O
A
B
C
Angle Addition Postulate
• Postulate 1-8: Angle Addition Postulate
2) If angle AOC is a straight angle, then…
180m AOB m BOC
A C
B
O
Congruent Angles
• congruent angles—angles with the same measure
Notation:
1 2m m measure equal sign
1 2 no measure congruency symbol
Ex 2: Solve for the missing angle
a)
21
B
A
C
1 42
88
m
m ABC
Find 2m
b)
S
W
R
T
50
125
m RST
m RSW
Find m TSW
88 42 46
125 50 75