Name:!!
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9/3/13!
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Figure
Point
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Unit 1 - Geometry
Notes: The Building Blocks of Geometry!
Notation
Picture
Definition
A point marks a place in space.
It has no length, no width, no height
(0 dimensional).
Name it with one single capital letter.
Line
A line is straight and infinitely long.
It has length but no width and no height
(1 dimensional).
A line can be named using any two points that lie
on it.
A line can also be named with a single lower
case letter.
Segment
A part of a line that has two endpoints.
A segment is named by its endpoints.
length of
a
segment
Ray
If a segment is named without the segment
symbol, it means the length of the segment.
A part of a line that has one endpoint.
A ray is named using two letters: its endpoint
and another point on the ray.
Two rays are the same if: __________________
and ____________________________________
Angle
An angle is formed by two rays with a common
endpoint. The endpoint is the vertex of the
angle.
An angle is named in one of three ways:
1. using the vertex,
2. using three letters- the vertex must be in
middle
3. using a number
Figure
Notation
Picture
Definition
Plane
A flat 2 dimensional surface. It has length and
width, but no height.
Three non-collinear points can be used to name a
plane. A plane can also be named with one
capital letter.
Problems:
1. !
Draw and label each of the following:
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A. !
a line that has points A, B, and C on it!
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B. !
a ray that begins at P and goes through points Q and R!
C.
a segment that starts at C, goes through O and A, and ends at T
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2. !
How does a segment differ from a line?
3. !
How does a segment differ from a ray?
4. !
How many points does a line contain?
5. !
How many points determine a line? Another way to ask this question is, “How many points
do I have to draw on the board before you’ll know EXACTLY what line I want you to draw?”
6. Suppose the two rays of an angle go in opposite directions. What do they form?
7.
SN refers to a ____________. Name it in three other ways.
S
8.
N
W
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QR is shown below.
P
(a)
Q
R
S
QS refers to a _____________________. Shade it on the line above.
Another name for that very same __________________ is ______.
(b)
Name 5 other segments (ALL DIFFERENT FROM EACH OTHER) on PQ .
9.
Give three names for this ___________.
How do you know that all three names that you gave above are really for the same ray?
You try the following multiple choice: circle all answers that are correct. There is often
more than one correct answer!!
1.
BC refers to a _________. Another name for it is:
(a)
2.
BE
(d)
CE
DA
(b)
AD
(c)
BC
(d)
AD
EC
(b)
BC
(c)
CA
(d)
CB
CE
(b)
CE
(d)
EC
(c)
EC
AE refers to a ____________. Another name for it is:
(a)
6.
(c)
The distance between C and E can be written as:
(a)
5.
BD
The ray opposite CE is called:
(a)
4.
(b)
AD refers to a _________________. Another name for it is:
(a)
3.
CB
CD
(b)
BC
(c)
AD
(d)
ED
(c)
DE
(d)
AB
The ray opposite BA is called
(a)
BE
(b)
EB
Name:
9/3/13
Geometry
Unit 1 -Fundamentals
HOMEWORK # 2 – Building Blocks
Use this picture to answer the questions on this page.
1.
2.
a.
Name the ray that starts at C and goes right.
b.
Name in two different ways the ray that starts at C and goes left.
c.
Name the two opposite rays that meet at B.
d.
Are BC and BD the same ray? If yes, give the two reasons why they are. If not,
explain which of the two reasons is not true.
e.
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Are BC and CD the same ray? If yes, give the two reasons why they are. If not,
explain which of the two reasons is not true.
f.
AB refers to a _________. Name it in three other ways.
g.
Name the ray opposite to CA .
Which of the following pairs are the same? Choose all the ones that are the same:
(a)
AB and BA
(b)
AB and BA
(c)
AB and BA
(d)
AB and BA
3.
What does AB refer to?
What does AB refer to?
4.
5.
Fill in the blank with point, line, segment, ray or plane.
(a)
a piece of spaghetti is a real-world example of a ___________
(b)
a poppy seed on a bagel is a real-world example of a ___________
(c)
a beam of light from a light bulb is a real-world example of a __________
(d)
the top of your desk is a real-world example of part of a __________
Now you find real-world examples for each of the following:
A point:
A segment:
A ray:
Part of a plane:
Angle:
6.
Draw two lines l and m that intersect (cross each other).
Now look at where they intersect (or cross). That place is a _______________ (choose
from ray, segment, line, point, plane).
7.
Can line l have a midpoint? WHY???????????????????
8.
Some algebra review… Solve for x in each equation without a calculator!!!
(a)
3x + 1 = 91
(b)
2x = 5x – 4
(c)
2
x + 5 = 25
3
3x
x
– 2 =
3
d) 5
(e)
3x – 1 + x = 5x - 9
f) 2x = 3x – 1
You must show all your work to receive any credit!
9. If the legs of a right triangle are 3” and 4”, what is the triangle’s area?
10. Evaluate x – y
2
z
for x = -4, y = 3 and z = 2
3. I wish to leave a 15% tip on a bill that comes to $18.00.
How much of a tip
should I leave?
4. Multiply (x – 3) (x + 7)
5. Make up a “word problem” for which the following calculation is needed:
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
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