Download What is Geometry? Understanding Angles

Aim: What is Geometry?
Do Now: Write an algebraic
expression for each of this
phrases:
3 more than w
r decreased by 2
the product of 5r and s
twice x decreased by 10
Aim: What is Geometry
Course: Appl. Geo.
geo metreinFrom the Greek
- “To measure
the earth.”
Aim: What is Geometry
Course: Appl. Geo.
Geometry Basics
Undefined Terms
Point
- Location, it has
no dimension
•P
Straight Line
C
A
- Collection of
points; extends
indefinitely in
both directions
D
B
AB - symbolically
Collinear – Points that lie on same line - A,
B, C, D are collinear.
Plane
A
B
•x
D
P
•y
C
- A set of points
suggested by a
flat surface P or
ABCD
Aim: What is Geometry
Course: Appl. Geo.
Coplanar – Points
and/or lines
that lie on
same plane - points x and y are coplanar
Geometry Basics
Line Segment
A
B
- Part of a line;
between two
points on a line
AB
Midpoint
M
E
EM  MF
Ray
F
- A point on a line
segment that is
equidistant from
the endpoints of
the line segment
- A part of a line
that has one
G
H
endpoint and
extends
GH
indefinitely in
the other
 - congruent
direction
Course: Appl. Geo.
exactly sameAim: What is Geometry
size and shape
Refer to diagram below in answering:
E
C
G
S
R
P
O
D
B
A
F
H
1. Which lines intersect at Point R?
CD & GH
2. Name 3 rays with endpoint S.
SD
SC
SE
3. Name 3 line segments on AB.
AP PO PB
4. Which line intersects EF?
Aim: What is Geometry
CD
Course: Appl. Geo.
M is the midpoint of AB
A
12
M
B
3x + 3
1. If AB measure 8”,
find the length of AM
of MB
4”
4”
2. If AM measures 10 feet,
find the length of AB
of MB
20’
10’
3. If AM = 12 and MB = 3x + 3,
find the value of x
12 = 3x + 3
9 = 3x
3 =x
Aim: What is Geometry
Course: Appl. Geo.
Model Problem
A
M
B
2x + 18
The length of AB is 2 x  18. How
long is it from A to M , the midpoint
of AB?
Aim: What is Geometry
Course: Appl. Geo.
Aim: What’s your angle?
Do Now:
Use sketchpad to draw and
measure angles
Aim: What is Geometry
Course: Appl. Geo.
B
O
A
Vertex
Angle - Two rays that have the
same endpoint, called a vertex
To identify an angle use the
symbol  and letters of the rays.
The vertex letter is in the middle.
Ex. AOB or BOA
Aim: What is Geometry
Course: Appl. Geo.
What’s in a name?
C
B
D
E
O
What’s another name for
A
AOC?
BOC?
DOA?
COD?
Aim: What is Geometry
Course: Appl. Geo.
B
protractor
O
A
Vertex
A common standard measure of an
angle is the degree - 1/360 of a
circle, written as 10.
A protractor is a tool used for
measuring the number of degrees
in an angle.
Aim: What is Geometry
Course: Appl. Geo.
Angle Types
C
B
D
E
O
Right Angle measures 900
A
AOC
Acute Angle - angle less than 900
AOB is an acute angle
Straight Angle - 1800
AOE
Obtuse Angle - less than 1800 but
AOD
greater than 900
Aim: What is Geometry
Course: Appl. Geo.
Sketchpad
With Sketchpad
1) Draw and label and measure
a) an acute angle
b) a straight angle
c) a right angle
d) an obtuse angle
2) Next to each, use the Text tool to
type a definition of each.
Example: ‘an acute angle is an
angle that measures . . . . (you fill
in the rest)’
3) Type your name at the bottom of
the sketch and save to flash
drive. Aim: What is Geometry Course: Appl. Geo.
What’s my name?
C
B
D
E
O
A
Name two right angles
Name as many acute angles as possible
Name 2 obtuse angles
Name a straight angle
Aim: What is Geometry
Course: Appl. Geo.
Model Problems
Determine the type of angle and
then estimate the measure of each.
A
C
B
C  D
Angles that are equal in
measure are congruent
Aim: What is Geometry
Course: Appl. Geo.
D
Angle Types
C
B
D
E
O
A
Adjacent Angles - Two angles that
have the same vertex and share a
common side
AOB & BOC
BOC & COD
COD & DOE
Linear Pair - Two angles that are
adjacent and supplementary
ex. AOB & BOE
Aim: What is Geometry
Course: Appl. Geo.
Addition Postulate
C
B
D
E
O
A
AOB + BOC = AOC
If mAOB is 37o and mBOC is 53o,
what is the measure of AOC?
If mBOC is 33o and mCOD is 63o,
what is the measure of BOD?
Aim: What is Geometry
Course: Appl. Geo.
Model Problems
Q
P
V
N
M
If mMQV = 90 and mVQP is 35,
what is mMQP?
If mMVQ = 55, what is mQVP?
Judging by appearances, name
a) two acute angles
b) two obtuse angles
c) two right angles
Aim: What is Geometry
Course: Appl. Geo.
Model Problems
Q
P
V
M
N
MVP is a straight angle. If mMVQ
is xo and mQVP is 2xo, what is value of x?
If mMNP = 165 and mMNQ = 2x – 3
and mQNP = 2x + 7, what is value of x?
Aim: What is Geometry
Course: Appl. Geo.