Chapters 2.1 and 5.4
CONDITIONAL STATEMENTS
CONDITIONAL
An IF-THEN statement
hypothesis part following if
conclusion part following then
If hypothesis, then conclusion.
Conditional Example
If an angle is a right angle,
(hypothesis)
then its measure is 9
2.4
PROPERTIES
AND
PROOFS IN
ALGEBRA
Euclid the father of
geometry
wrote The Elements
about 300 BC
a book of 13 chapters which we
use today for our definitions and
postulates and theorems
PROOFS
Given: 2x + 3 = 11
Prove: x = 4
statements
1.
2.
3.
4.
5.
2x
2.4
OVERLAPPING
SEGMENTS
AND ANGLES
THEOREMS
A
3
B
8
3
C
D
Compare AB and CD
Compare AC and BD
Which segment overlaps AC and BD ?
OVERLAPPING
SEGMENT THEOREM
A
B
C
D
If AB CD AC BD.
If AC BD AB CD.
Use for & must use
Reflexive Property
first.
Given : AB C
2.4
OVERLAPPING
SEGMENTS
AND ANGLES
THEOREMS
3
A
B
8
3
C
D
Compare AB and CD
Compare AC and BD
Which segment overlaps AC and BD ?
OVERLAPPING
SEGMENT THEOREM
A
B
C
D
If AB CD AC BD.
If AC BD AB CD.
AB CD
A
B
C
D
AB = 10
BC = 25
find BD.
35
AC = 50
BC = 30
Angle
Theorems
If two angles form a
linear pair, then they
are supplementary.
Given: 1 & 2 are a linear pair
Prove: 1 & 2 are supplementary
1
2
A
C
B
1 & 2 are a linear pair of angles formed
by opposite rays BA and BC. Opposite rays
form a straight angle
Angle
Theorems
Paragraph
Proof
Given: 1 & 2 are a linear pair
Prove: 1 & 2 are supplementary
1
2
A
C
B
1 & 2 are a linear pair of angles formed
by opposite rays BA and BC. Opposite rays
form a straight angle so mABC = 180.
By angle addition, m ABC = m1 +
X
#1
Prove: AB + BC = CX
1.
2.
3.
4.
AC CX
AC = CX
AB + BC = AC
AB + BC = CX
A
1.
2.
3.
4.
B
C
Given
If
Segment Addition
Substitution
Q
#2
Prove: WB = WZ - 4
A
W
B
C
1. WA = WC , CB = 4
1. Given
2. WB + BC = WC
2. Segment Addition
3. WB + 4 = WC
3. Subst
Identify the Postulate or Reason to justify the
following.
1. If 7y + 3 = 8 and 3 = 3, then 7y = 5
subtraction
2. WX = WX
reflexive
3. If B is the midpoint of DE then DB = BE
Definition of Midpoint
4. If 2(f + 3) = 5(w 2) then 2f + 6 = 5w 10
distributive
Distance Formula
The distance d between
two points A(x1 , y1 ) and B(x 2 , y 2 ) is :
d (x 2 x1 ) y 2 y1
2
2
THE DISTANCE FORMULA HOW
DOES IT WORK?
ABC is a right triangle .
Using the distance formula we will find the length
Use the Pythagorean Theoremof
Chapter 1.7
BASIC CONSTRUCTION
Intersect at right angles.
90
t
s
st
segment or line that is:
- forms a 90
divides the segment
into 2 segments
A
B
C
B is the midpoint of AC
A ray that divides
an into 2 s.
A P is the bisector .
M
P
30
1
2
A
30
T
MAP TAP
Geometry K
Name _
Graphing Review Day
Period_ Date _8/23_
_
Slope-Intercept Form
y = mx + b given y-intercept (b) and slope m.
Distance Formula d ( x2 x1 )2 ( y2 y1 )2
y
y y
or m 2 1 given points (x1,y1) and(x2,y2)
x
x2 x1
1. Find the slope of the line co
K Geometry
Ch. 1.3 & 1.4 Points, Lines and Planes
FILL IN THE BLANKS:
I. A
p i AA
represents a specific location in
9. A set of f our or more points not on t he
"
is a s traight path of p oints with no
!0. The 3 u ndefined terms are f p : A% .
P
and
endpo
THE LIST
Overlapping segment Thm
If an angle is comp to
Addition +
(OST) ()
's it is comp to each
Subtraction
of the 's
Overlapping angle Thm
(OAT) ()
Multiplication X
If ll lines AIA
Division
If ll lines CA
Angle Addition (= only)
Distributive
If ll
Chapter 1.3
POINTS , LINES
AND PLANES
Lines
Points
Planes
SPACE
(THE SET OF ALL POINTS)
POINT
a location in space
has no size
Name a point with a capital
letter and represent it with a
dot A (point A)
LINE
Straight path of points
No thickness
Extends infi
Chapter 1.4
SEGMENTS,
RAYS, PARALLEL
LINES AND
PLANES
RAY
part of a line
one endpoint
extends infinitely in one direction
A
B
AB
SEGMENT
part of a line
2 endpoints and all points
between them
AB
A
or
BA
B
OPPOSITE RAYS
2 collinear rays with the same
en
Chapter 1.5
MEASURING
SEGMENTS
CONGRUENT
same size
same shape
CONGRUENT SEGMENTS
same length
A
5
B
C
5
D
AB CD
A B CD
MIDPOINT OF A
SEGMENT
A point that divides
the segment into 2
segments.
midpoint
A
B
C
AB BC
Find x.
10x-2
A
9x+6
B
C
10x - 2 = 9x + 6
2
rays with a common
endpoint
rays meet at the vertex
vertex
1
A
CAT
TAC
Name this angle:
A
C
1
T
Name
these angles:
2
E
BED
DEB
B
2
D
E
Name
the angles:
N
3
P
4
A
T
ACUTE
less than 90
RIGHT
90
OBTUSE
greater than 90
less than 180
STRAIGHT
180
have th
=
Overlapping angle Thm
(OAT) ( )
I f ll lines AEA
Subtraction
Angle Addition (= only)
I f ll lines SSEA supp
Multiplication
(may assume VA and LP by
picture or statement)
If AIA ll lines
+THE L IST
orX
Addition
Division
Distributive
Substitution
Reflex