Download Notations and Segments

Name _________________________________________
Period ____
8/22 – 9/2
NOTATIONS AND SEGMENTS
1) Define, identify or illustrate the following terms
Undefined term
Segment
Point
Endpoint
Line
Ray
Plane
Opposite Rays
Collinear
Postulate
Coplanar
Distance
Length
Congruent
Between
Midpoint
Bisect
Segment bisector
Dates, assignments, and quizzes subject to change without advance notice.
Monday
22
First Day of Class
29
Tuesday
23
Understanding Points,
Lines, and Planes
Block Day
24/25
Segment Addition and
Bisectors
26
30
31/1
2
Distance
Midpoint
Review
Friday
QUIZ
More Practice
TEST 1
Monday, 8/22/11
Welcome to Geometry
Expectations and Procedures
Supplies Needed
ASSIGNMENT: Get supplies organized
Completed:
Tuesday, 8/23/11
Chapter 1 Section 1: Understanding Points, Lines, and Planes
2) I can use proper notation and symbolism for geometric structures.
3) I can draw geometric structures.
4) I can determine the relationships between points, lines, and planes.
ASSIGNMENT: Points, Lines, and Planes Worksheet
Completed:
Wednesday or Thursday, 8/24-25/11
Chapter 1 Section 2: Measuring and Constructing Segments
5) I can solve problems using Segment Addition Postulate.
6) I can solve problems using segment bisector/midpoint.
ASSIGNMENT: pg. 17-19 (1-4, 6-10, 24-27)
Completed:
Friday, 8/26/11
Quiz and Practice Day
Quiz: Sections 1 and 2
Grade:
ASSIGNMENT: Practice Worksheet
Completed:
GL
Monday, 8/29/11
Chapter 1 Section 6: Midpoint and Distance in the Coordinate Plane
5) I can find the length of a segment on the Coordinate Plane.
ASSIGNMENT: Pg 47 - 48 (6,7, 16-20)
Completed:
Tuesday, 8/30/11
Chapter 1 Section 6: Midpoint and Distance in the Coordinate Plane
5) I can find the midpoint of a segment on the Coordinate Plane.
6) I can find the missing endpoint of a segment given the midpoint on the Coordinate Plane.
ASSIGNMENT: pg. 47 (2-5, 12-15)
Completed:
Wednesday or Thursday, 8/31 – 9/1/11
Review Day
Completed:
ASSIGNMENT: Review for Test IN CLASS
ASSIGNMENT: Review for Test AT HOME
Completed:
Friday, 9/2/11
Test Day
Unit 1 TEST: Notations and Segments
Grade:
Notations Notes
I. Vocabulary Reminders
1. Collinear means ____________________________________________________________________.
2. Coplanar means ____________________________________________________________________.
3. If you add “non” in front of the word it means ____________________________________________.
II. Naming Geometric Structures
You name a point by ___ _________ letter, ex.
would be named ____.
A line is named by ____ ___________ with a _________ above or a _____ _______ script letter.
ex
could be named __________ or __________ or __________.
A plane is named by _________ _________________ points or a _________ script letter.
ex
could be named __________ (in any order) or __________.
A segment is named by ____ ___________ with a _________ above.
ex
could be named __________ or __________.
A ray is named by ____ __________ and __________ ____________ point with a _________ above.
ex
could be named __________ or ___________.
_____________________ rays are rays that have _______________________ and go ______________ directions.
III. Relationships of Geometric Structures
Through any _____________ points there is ____________ _______________ line.
Through any ______________ ___________ points there is _____________ _____________ plane containing them.
If two lines intersect, then they intersect in _________ ___________ ___________.
If two planes intersect, then they intersect in _________ ___________ ___________.
IV. Sketching: Sketch each structure.
1.
suur
CS
5.
suur uur
RU ⊥ ST
2.
uuur
SG
3. WO
6.
EF intersecting ℜ at B
4. MBD
7.
suuur
ℑ intersecting GEO at GM
Vocabulary Organizer
Term
Picture
Description
Label
Other
It is a location and
has no size.
Represented by a
A
Name with a capital
letter
dot
.
B
Ä
C
B
Plane
A
C
P
,
BC
CB
or Ä
A flat surface
that has no
thickness and
extends forever
A part of a line that
consists of two
points and all points
between them.
B
C
suur suur
BC , CB
Name with either a
lowercase cursive
letter or 2 points
under a line.
A point at one end
of a segment or the
starting point of a
ray.
or
Name with 2 points
under a segment.
Term
Picture
Ray
Collinear
A
B
C
B
C
Description
uuur
BC
D
Objects that lie on
the same plane
Same size and same
shape
C
Noncollinear
A
B
Label
Other
Points that do
not lie on the
same plane.
Noncoplanar
To divide into
two congruent
parts
The point
halfway
between two
given points
Midpoint
Leave box empty
Opposite Rays
The set of all
possible points;
made up of
infinite planes
Two rays that
have a
common
endpoint and
form a line.
Notations Examples
POINTS, LINES, & PLANES WORKSHEET
1. Tell whether each object suggests a point, line, or plane:
a) a parking lot __________________
c) the tip of a pencil _____________
e) a basketball court _____________
g) a tightly stretched ribbon _______
b.
d.
f.
h.
the edge of a table ________________
a long clothes-line ________________
the floor in your bedroom __________
the tip of a nail __________________
2. Name each of the following using the correct symbols:
a) ________________
b) ________________
c) ______________
d) ________________
e) _________________
f) ______________
3. Write the symbol for the following descriptions:
a) The line that contains the points U and V __________________
b) The ray with endpoint G and passing through point T _________________
4. Use the figure on the right to name each of the following:
a) two planes _______________________
b) a plane that contains A, C, & E _______________
c) four coplanar points ___________________
d) a plane containing B ___________________
e) intersection of planes U and X ______________
f) two names for plane U ____________________
5. Use the figure on the right to name each of the following using correct symbols:
a) five points ___ , ___ , ___ , ___ , ___
b) three different lines _____, _____, _____
c) six different rays _____, ______, ______,
_____, ______, ______
d) eight line segments ______, ______, ______,
______, ______, ______, _______, ______
e) three segments that contain point G.
______, ______, _______
f) two lines that contain point K. ______, _______
g) three collinear points ___, ___, ___
h) point on MG
____
i) line that contains N & H _______
6) Draw and label each of the following:
a) a line containing points K and S.
b) a ray with endpoint K that passes
through point L.
c) a segment with R and U as endpoints
d) SK
e) 3 coplanar lines that intersect at one point
f) two lines that do not intersect
g) a pair of opposite rays that contain S.
h. plane H containing two lines that
intersect at point M.
Unit #1 Practice Worksheet
x–3
1. Given the line segment, solve for x if
AC = 6x + 23
A
2. Given the line segment, determine if B is
the midpoint and justify your answer.
7x + 12
B
C
3y – 4
2y + 5
A
B
C
7y – 5
3. Find AS if H is between A and S and AH = 5b − 1 , HS = 12b + 7 , and AS = 8b + 9
4. E is between DF , DF = 2, DE = 2y, and EF = 8y – 3. Is E the midpoint? Justify your answer.
x
5. Find MN
M
2.5x
N
R
5x – 3
C
7. GH bisects CF , CF = 2y–2, and CD = 3y–11. Find CD.
D
G
F
Use the following picture to solve for the variable in questions #8–#10.
R
8. RS = 7y – 4, ST = y + 5, RT = 28. Find y.
S
H
T
9. RS = 3x + 1, ST =
1
x + 3 , RT = 18. Find x.
2
10. RS = 3 z + 6 , ST = 4 z − 3 , RT = 5 z + 12 . Find z.
11. Find the error in Anthony’s problem and fix it to get the correct answer.
A is the midpoint of MP . MA = 3 x + 2 and MP = 5 x + 8 . Find x.
MA = MP
3x + 2 = 5 x + 8
2 = 2x + 8
−6 = 2 x
−3 = x
12. Which of the following equations could NOT be used to set up the following problem?
V is the midpoint of MP . MV = 3 x + 4 , VP = 5 x − 6 and MP = 8 x − 2 .
A) 3 x + 4 = 5 x − 6
M
V
B) 10 x − 12 = 8 x − 2
P
C) 3 x + 4 = 8 x − 2
D) 8 x + 2 = 2(3 x + 4)
13. Two lines intersect in exactly one__________.
14. Two planes intersect in exactly one ____________.
15. Any ________ __________ make up a plane.
Use the picture at the right to answer questions 16 – 19.
16. Give another name for plane R. __________
17. Where do planes R and P intersect? _____________
suur
18. Give another name for line BA . __________
19. Name three noncollinear points.____________
Distance and Midpoint Examples
Review Ch. 1 Segments
*** You must study all vocabulary !!! ***
DISTANCE FORMULA d = ( x2 − x1 ) 2 + ( y2 − y1 ) 2
1. Find AB where A(1, -2) and B(-4, -4)
2. Find XY where X(-2, 7) and Y(-2, -8).
3. Find FG
4. Find RS
4b. Is FG ≅ RS ?
 x1 + x2 y1 + y2 
,
 = MIDPOINT
2 
 2
FIND MIDPOINT!! 
5. M is the midpoint of AB where A(1, -2), M (?, ? ) and B(-5, -4). Find the coordinates of midpoint M.
6. M is the midpoint of VW where V(2, -1), M(?, ?), and W(-4, 8). Find the coordinates of midpoint M.
7. M is the midpoint of LN where L(-3, -1), M(0, 1), and N(?, ?). Find the coordinates of endpoint N.
Find the following using the picture on
the right (8-14):
8. Name four coplanar points
9. Name the line containing C and D
10. Name a pair of opposite rays
11. Name the points that determine
plane U
12. Name the intersection of planes U
and X
suur
suur
13. Name the intersection of AC and BD
14. Name three collinear points
15. Y is between X and Z, XY = 13.8 and XZ = 21.4. Find YZ . Draw & label a picture.
16. Q is between P and R. PQ = 3x, QR = 6x + 4, and PR = 14x – 6. Find PR. Draw & label a picture.
17. U is the midpoint of TV , TU = 3x +4, and UV = 5x – 2. Find TU, UV, and TV.
18. E is the midpoint of DF , DE = 9x, EF = 4x + 10, and DF =36. Which of the following equations are
correctly set up to solve for x?
I. 9x = 4x +10
II. 9x = 36
III. 9x + 4x + 10 = 26
IV.
2(9x) = 36
V.
4x +10 + 4x + 10 = 36
19. The three undefined terms in geometry are _______________________, _______________, and
______________________.
20. The intersection of two lines is a ________________.
21. The intersection of two planes is a ________________________.
22. Draw
with E intersecting
at point E.
23. What do opposite rays look like?
24. Given that point D is between A and C. If CD = 4x+6, AD = 2x-8 and AC = 34, Is CD=AD? Justify your answer.