Download Geo Unit 1

Geometry
Unit 1
Tools of Geometry
Unit
Unit 1I
Points
•
•
A
Collinear
B
A
Noncollinear
B
B
•
Coplanar
•
Noncoplanar
A
A
B
Unit
Unit1I
Lines
•
Coplanar
m
p
m
•
p
Noncoplanar
m
•
Intersection of two lines is a point
A
p
Unit
Unit1I
Planes
• Intersection of two planes is a
line
Unit
Unit1I
Distance between Points
•
•
AB = |a - b| or BA = |b – a|
d
x2  x1    y2  y1 
2
2
a
b
A
B
y
d
(x2, y2)
(x1, y1)
x
Unit
Unit1I
Segment Addition
• PR = PQ + QR
QR
PQ
Q
P
R
PR
Unit
Unit1I
Constructing Segment Bisectors
A
B
M
A
M
B
A
M
A
M
B
B
A
B
M
A
M
B
Unit
Unit1I
Parts of an Angle
Terminal Ray
ON
Exterior
Interior
Vertex
Initial Ray
Unit
Unit1I
Classification of Angles
•
Acute
0º < θ < 90º
•
Right
θ = 90º
•
Obtuse 90º < θ <180º
•
Straight θ = 180º
θ
θ
θ
θ
Unit
Unit1I
Angle Addition
m ABC  m ABD  m DBC
A
B
D
C
Unit
Unit1I
Protractor
Outer Scale
Inner Scale
Unit
Unit1I
Protractor
•
•
Two Scales
Measures in Degrees (˚)
Unit
Unit1I
Constructing Angle Bisectors
Unit
Unit1I
Special Pairs of Angles
Corresponding Angles
Vertical Angles
Two angles whose sides
form two pairs of opposite
rays.
Two angles on the same side of a
transversal (m); but one angle (1) is interior
of the parallel lines ( n & p) and the other
angle (2) is exterior.
1 and  3
 2 and  4
p
n
Exterior
2
1
3
4
m
1
Interior
Exterior
2
Transversal
Unit
Unit1I
Special Pairs of Angles
Adjacent Angles: have a common vertex,
a common side, and no common interior
points.
8
4
1
2
3
Yes
5
7
6
No
Unit
Unit1I
Special Pairs of Angles
Complimentary
Sum of angles is 90º
Supplementary
Sum of angles is 180º
4
3
2
1
Unit
Unit1I
Perpendicular and Parallel Lines
y
• Slope
y2  y1
m
x2  x1
• Perpendicular lines: two
lines whose intersection
is a right angle.
• Parallel lines: two
coplanar lines that do
not intersect.
(x2, y2)
m
(x1, y1)
ml  m p  1
x
l
p
ml  m p
l
p
Unit
Unit1I