Transcript Plane Geometry Unit 1 – Chapter 1

SECTION 1.2 NOTES
Postulate or Axiom – a rule that is accepted without proof.
Ruler Postulate
 The points on any line can be matched to real numbers,
that real number is known as the coordinate of that point.
 The distance between any two points A and B, is written
as AB and is the absolute value of the difference of the
Names
coordinates of A and B.
A
x1
Coordinates
DISTANCE
AB = |x1 – x2|
B
x2
SECTION 1.2 NOTES
Segment Addition Postulate:
 Between - is only when three points are collinear
 If B is between A and C, then AB + BC = AC
 If AB + BC = AC, then B is between A and C.
AC
B
A
AB
C
BC
SECTION 1.2 NOTES
Congruency:
Congruent Segments – line segments that have the same
length.
Equal vs. Congruence
AB = CD
A
B
lengths are equal
C
D
Mathematical Notation: Congruent
AB ≅ CD
Segments are congruent
SECTION 1.2 NOTES
Using the ruler postulate...
W
-10
Y
X
-8
-6
-4
-2
0
2
4
Z
6
Find:
1) WX
2) XY
3) WY
4) ZW
8
10
SECTION 1.2 NOTES
Points G, H, I, J and K are collinear. GK = 24, HJ = 10, and GH =
HI = IJ. Find each length
24
G
H
I
10
K
J
1) HI
2) IJ
3) GH
4) JK
5) IG
6) GK
SECTION 1.2 NOTES
Find RS, QS, and TV using the following information:
S is between T and V. R is between S and T. T is between R
and Q. QV = 23, QT = 8, and TR = RS = SV
V
S
R
Q
T
23
?
8
SECTION 1.2 NOTES
Point J is between M and N. Find the length of JM and JN
given the following information. JM = 7x + 2, MN = 64,
and JN = 2x – 1.
M
N
J
64
7x + 2
2x – 1
So (7x + 2) + (2x – 1) = 64
9x + 1 = 64
9x = 63
x=7
JM: 7(7) + 2 = 51
JN: 2(7) – 1 = 13
SECTION 1.2 NOTES
Point M is between V and W. Find the length of VM and MW,
given the following information. VM = 4x – 1, VW = 30,
and MW = 3x + 3.
V
W
M
30
4x – 1
3x + 3
So (3x + 3) + (4x – 1) = 30
7x + 2 = 30
7x = 28
x=4
MW: 3(4) + 3 = 15
MV: 4(4) – 1 = 15
CONCEPT CHECK
P. 10-11
#3 – 6
“Guided Practice”
HOMEWORK
P. 12-13
#6 - 30
(Omit #12)