Transcript 1.1 Building Blocks of Geometry

Geo Warm-Up
Make & label a chart and answer the
question in a complete sentence
John, Harry and Phil are married to Sally, Nancy &
Arlene, but not necessarily in that order. John,
who is Sally’s brother, has 5 children. Nancy who
is a certified public accountant wants to wait
several years before starting a family. Harry is
married to John’s sister. Who is Phil married to?
Solution

John is married to Arlene


Harry is married to Sally


(Sally is his sister, he has
children and Nancy is waiting
to have children)
(John’s sister is Sally)
Phil is married to
Nancy.
John
Sally
Nancy
x
x
Harry
Phil
x
x
Arlene
x
x
1.1 Building Blocks of Geometry
Examples


There are 3 undefined terms
in geometry: point, line, and
plane. These terms can be
described but they can’t be
defined.
A point is a “dot”. It has no
size, just a location. A point is
named by using a capital
letter.
A
Examples
1.1 continued


A line is made up of an infinite
number of points and is
considered to be straight. To
name a line, pick any two
points on the line (in any order)
and place a ↔ above them.
A plane is a flat surface that
extends infinitely along its width
and length. You represent it
with a 4-sided figure. To name
a plane, a script capital letter is
used.
A
B
AB or BA
C
AC or CA
BC or CB
P
Examples
1.1 continued

Collinear points are
points on the same
line.
 ANY
2 points will
ALWAYS be collinear

Coplanar points are
points on the same
plane.
 ANY
3 points will
ALWAYS be coplanar
D
Are the following points
collinear?
YES
1) A and B ______
NO
2) A and B and D ___
YES
3) A and B and C ____
F
E
I
G
H
P
Are the following points
coplanar?
1) E and F and G ______
YES
YES
2) E ,F ,G, H ______
3) F, G, H, I ____
NO

A ray is a part of a line that
starts at a point called its
endpoint, and then extends
infinitely in one direction.
To name a ray, you need
two points. The first point
is its endpoint. This
indicates where the ray
starts. The other point is
any other point on the ray.
You then put a → symbol
above those two points.
A
B
C
Ray AB starts at A
extends towards point
B - another way to
say AB is ____
AC
If you say CA that is a
different ray

A line segment is a part of
a line with a beginning and
A
an end. The point at the
B
beginning and the point at
the end are called the
C
endpoints. To name a
segment you use its
AB or BA
endpoints (in either order)
then place a − symbol
CB or BC
above them.
AC or CA

Two segments are congruent if
they have the same length. The

symbol for is congruent to is_____.
Never use a congruent symbol with
a number!!!

There are 2 ways to write “the length
of a segment”
 Equal
sign
 Or mAB = “m” stands for measure of”

To bisect an object
means to cut it in half.
A
D
 You
can bisect an angle
or a line segment
C
B
 To
show a bisector you
mark the congruent parts
BD is the angle
bisector of < ABC

A midpoint of a segment is a
point that is halfway between
the endpoints. A midpoint
bisects the segment.
A
B
is the midpoint of AC
 Formula for midpoint
 x1  x2 y1  y2 
,


2 
 2
B
C
1.1 Summary

Write down in complete sentences and in
your own words 3 things that you learned
today.
1.2 Poolroom Math – pick up
protractor on front table
An angle is formed by two rays
that share a common endpoint.
The vertex of the angle is the
common endpoint of the two rays.
37º

Angles are measured in degrees.
Angles that have the same
measure are called congruent
angles.
1.2 continued

49º
49º
An angle bisector is a ray that
divides an angle into two
congruent angles.
1.2
Continued
3 methods to name an angle
1. Use three points that make up that angle, the vertex
must be in the middle
C
< ABC or < CBA
B
A
2. Use the number or letter in the interior of the angle
<2
2
3. Use a single letter (be careful about other angles)
A
F
1.2 continued
Complete Example 1 in your notes.
One of you will be called to the
board.
R
U
1
V
T
1.2 continued
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Complete example #2.
Name each angle bisector and the
angle it bisects.
0
b) If m YCD  20 , then m DCA  ____
a)
N
D
A
Y
C
1.2 continued
A Protractor is a geometric tool used to
measure an angle and to draw an
angle.
Follow the directions on your notes and
measure the two angles.
After you have measured the angles,
follow the directions from Example 3
and draw two angles.
1.2 Summary

Write down in complete sentences
and in your own words 3 things
that you learned today.
1.1 1.2 Homework
Page 33-34 #2-15, 18-27
 Page 42-44 # 1-24,30-33
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