Download Section - cloudfront.net

Section: 1.2
Name:
Topic: Points, Lines and
Class: Geometry 1A
Planes
Period:
Standard: 1
Date:
Points
1. In the space below put a point and label it Point A. A point is
a __________ at a specific _________________.
Segments
2. Mark another point as Point B.
3. Connect Point A to Point B. This is _______________ AB or
_____.
A ___________________ is a _____________ of a line with
_______ endpoints.
Lines
4. Draw two more points C and D and draw a line through these
points.
A line extends in two directions ___________________.
We write this ________.
Note: Although a ________________ can be measured by its
length, a ________ cannot since it goes on _______________.
Rays
5. A ray is a part of a line that goes on forever in one
_________________.
Draw Ray EF or ______ in the space above. In this case, the
ray starts at E and continues past_________. (This is ______
the same as starting at F and continuing past Point E.)
1
Examples Name each point, line, segment and ray.
G
J
N

K
_______________ and
M

__________ can be
named in two ways.
H
L
Draw two points, A and B, on your piece of patty paper. Fold the patty paper so
that you get a line through your two points.
How many points does it
take to determine a line?
Did you need another point to make the line? What if you had
only had one point?
Place a third point, C, on the line.
The three points, A, B and C, are called __________________
because they are all on the ____________ _____________.
Choose a point, D, not on line AB. Fold a line through C and D.
What is the least number of points it takes to form a line? ______
(glue your patty paper here)
Name as many
lines as you can.
Naming a Line
2
Planes
Imagine the sheet of patty paper extending in all
__________________ forever. This is the idea behind a plane.
Naming a Plane You name a plane with a cursive capital letter or with three points.
1. Name your patty paper Plane P.
2. Fold plane P anywhere on the paper. Now we have two different planes.
Label the second plane R.
3. Glue your patty paper in the space below. Only glue down Plane P.
What is the intersection of
two planes?
Where do the two planes intersect?
Place points S and T on this intersection. Mark Point U in Plane P and Point V
in Plane R.
How many points does it
take to make a plane?
You must have _________ points that are _____-_____________
to make a plane.
What is another name for Plane P? _______________________
What is another name for Plane R? _______________________
Could we name either plane as Plane ST? Why?
How many planes can pass through line ST? ________________
3
Examples Use the picture below to determine planes, lines and points.
F
G
H
E
D
A
C
B
A. Shade Plane DCA.
B. Name Plane DCA another way. _______________________
C. Name the intersection of Plane HGC and Plane EFG. ______
D. Name the intersection of EF and DF . ________
E. List all points that are on Plane FGC. ___________________
F. Mark Point J so that it is collinear with Points A and D.
More on Rays
We know that a ray is a _________ of a line that extends in
_________ direction forever. What happens when you have two
rays that share their endpoint? There are three different ways this
could happen.
Case 1: A(n) ________________ is formed.
Case 2: A(n) ________________ is formed.
Case 3: A(n) ________________ is formed.
Summary/Reflection: Why do you think arrowheads are used when drawing or naming a line?
4
Section: 1.3
Name:
Topic: Parallel Lines &
Class: Geometry 1A
Planes
Period:
Standard: 1
Date:
F
G
H
E
D
A
Parallel Lines & Segments
C
B
EF and HG are parallel segments. What makes two lines or
segments parallel? ___________________________________
Name every segment parallel to DC . _____________________
Perpendicular Lines &
Segments
EF and EA are perpendicular segments. What makes two
lines or segments perpendicular? _______________________
Name a segment perpendicular to DC . ____________________
Skew Lines & Segments
EF and HB are skew segments. What makes two segments
or lines skew? _______________________________________
Name all segments skew to DC . _________________________
Parallel Planes
Planes DCA and FGH are parallel planes. What makes two
planes parallel? ______________________________________
Name a plane parallel to Plane DCF. ______________________
Summary/Reflection: Are all lines either intersecting or parallel? Explain.
5
Section: 1.4A
Name:
Topic: Measuring
Class: Geometry 1A
Segments
Period:
Standard: 1 & 12
Date:
Bisect a Segment
1. On your patty paper use a straightedge to draw AB .
2. Fold the patty paper so that Point A falls on Point B. Crease the fold to form
a line.
The fold line is the _________________ of AB .
_________________ The point where the fold intersects AB is the ______________ of
AB . Label this point C.
_________________ We can mark the two __________________ segments with tick
marks or write AC _____ CB .
Copy a Segment
3. Fold your patty paper so that you can trace over AB .
4. Mark the new segment A ' B ' . The prime marks signify which points are
_______________________.
When you copy a segment you make another segment with the
same _____________________. We can say AB _____ A ' B ' .
5. Glue your patty paper in the space below.
6
Coordinate on a Number
Line
The coordinate of a point is its _________________ and
___________________ from the ______________ (0) on a
number line.
Examples
A
-5
B
0
5
The coordinate of point A is -1.
A. What is the coordinate of point B? ________
B. Label point C at -4 and point D at 6.
Length of a Segment
The distance from one point to another is the length of the
segment joining them. The distance is given by the formula
Absolute value sign
The length of AB .
AB  ______  ______
The coordinate of A.
Examples
The coordinate of B.
C. AB  ______  ______ = ______________ = _______
D. AC = __________________________________________
E. CD = __________________________________________
Midpoint
To find the midpoint of a segment take the average of the two
endpoints.
Midpoint of AB =
AB
2
Examples The midpoint of AB = _____  _____ = ________
2
F. What is the midpoint of AC?
G. What is the midpoint of CD?
7
Segment Addition
If three points A, B and C are collinear and B is between A and C,
then AB + BC = ____________.
Draw a picture to
help you understand
the postulate.
Example A
J, M and D are collinear. D is between J and M. JD = 5. JM = 13.
What is DM?
1. Draw a picture.
2. Set up an equation.
3. Solve and check.
Example B
A, C and T are collinear. A is between C and T. CT = 26. A is the
midpoint of CT . What is AT?
Example C A, N and T are collinear. N is between A and T. AN = 2x – 6.
NT = x + 7. AT = 25.
What is x? _______
What is AN? ______
What is NT? ______
Measuring with a Ruler
Throughout this course you will need to measure segments with a
ruler. There are two units of measure we’ll use in this class –
_______________ and ______________________________.
The crayon is about
________ inches long.
The pencil is about
_______ centimeters
long.
8
Inches Inches are broken down into smaller fractional units. Segments
are usually measured in sixteenths of an inch, such as
5 10
 .
8 16
1 4

or
4 16
What is the measurement of the segment shown below?
Centimeters Centimeters are broken down into smaller units called millimeters.
There are _______ millimeters in one centimeter.
How many centimeters are shown in the brace below? _______
Examples Measure each segment below in inches and centimeters.
A.
B.
Summary/Reflection: On a number line, point Q has a coordinate 1 and T has a coordinate 17.
A is the midpoint of QT , B is the midpoint of QA , C is the midpoint of
QB , and D is the midpoint of QC . What is the coordinate of D?
9
Section: 1.4B
Name:
Topic: Measuring Angles
Class: Geometry 1A
Period:
Standard: 1 & 12
Date:
Angles
(_______)
An angle is formed by two ___________ that share a common
endpoint. This endpoint is called the ____________ of the angle.
B
1
A
C
Naming an Angle
There are many ways to name this angle - _______, _______,
______ or _______.
Protractor
One way to measure angles is in degrees (____). A protractor is
the tool used to ___________________ the opening of an angle.
MAKE A PROTRACTOR
Use fraction circles to make a
protractor. The measure for 0 is
already marked for you.
Measurement of angles is done
counterclockwise.
1. Since a circle is 360 you can
divide that by 2 to get the measure
of half a circle. Mark it on your
protractor.
2. If we split the circle into 3 parts.
How big is each angle? Mark the
protractor with these angles.
3. Now split the circle into 4 parts
and mark it.
4. Split the circle into 6 parts and
mark it. (Yes, we are skipping 5
parts.)
5. Split the circle into 8 parts and
mark it.
6. Split the circle into 12 parts and
mark it.
0
10
A common protractor is shown below. Notice that only the top half
of the protractor is used but two sets of numbers are displayed.
The ______________ of the angle is in the center of the small
circle at the bottom and the ______________ of the angle lines up
with the 0-180 line.
If you start from the left, you’ll use the _________ set of numbers.
Starting from the right, you’ll use the __________ set of numbers.
Examples
Use a protractor to measure the angles.
A.
B.
11
Types of Angles
Angles can be categorized by their measure.
Name of Angle
Degree Measure
Picture
Acute
Right
Obtuse
Straight
Congruent Angles and
Angle Bisectors
1. Using a straightedge draw an
obtuse angle in the middle of
a large piece of patty paper.
Label your angle DEF.
An angle bisector creates _______ _______ ______________.
DEG _______ GEF
2. Fold ray DE onto ray EF. The
fold should go through point
E.
3. Label the fold line EG where G
is in the interior of DEF.
4. Glue your patty paper into the
space below.
Angle Addition Postulate
If point G is in the interior of DEF, then
m_______ + m_______ = m DEF.
12
If point B is in the interior of AOC and AOC is a straight angle,
Straight Angles
then
mAOB + mBOC = ___________.
A
O
C
Examples A. In the picture below mDBC = 42 and mABD =73. What is
mABC?
A
D
B
C
B. In the picture below mEFG = 102 and ray FH is an angle
bisector. What is mHFG?
E
H
F
G
Summary/Reflection: Michael says that the angles measures in the picture below must be
wrong, since the first angle is “bigger” than the second. Explain in 2 – 3
sentences why Michael is incorrect in this thinking.
Angle 1
Angle 2
90
180
13
Section: 2.5
Name:
Topic: Proving Angles
Class: Geometry 1A
Congruent
Period:
Standard: 1 & 12
Date:
4
3
5
6
2
1
12
11
7
8
10 9
Vertical Angles
In the diagram above, 1 & 12 are vertical angles, while
1 & 11 are not. Name other vertical angles:
_____ & _____
_____ & _____
_____ & _____
_____ & _____
_____ & _____
 Vertical angles are formed by ______________________ lines.
 Vertical angles share a ___________________, but not a
_______________.
 Vertical angles are always ________________________.
Adjacent Angles
In the diagram above, 1 & 11 are adjacent angles. Name
three other sets of adjacent angles:
_____ & _____
_____ & _____
_____ & _____
 Adjacent angles share one ___________________ and their
_______________.
 Adjacent angles are _______ always ____________________.
14
Examples Which angles below are adjacent? Explain why the others are not
adjacent.
A.
B.
3
1
4
2
C.
6
5
Complementary
D.
7
8
The sum of complementary angles is ___________.
C
The sum of supplementary angles is ___________.
Supplementary
S
A linear pair is ______ adjacent ____________________ angles.
Linear Pair
Examples
A.
x
120
B.
2x
C.
5x + 10
70
2x – 5
15
Assumptions
What can you assume from a picture?
Picture
OK to Assume

1
2
NOT OK to Assume






3
4


5

6

Ways to remember
Complementary =90° and
Supplementary = 180°
Summary/Reflection: Can vertical angles be complimentary? Can vertical angles be
supplementary? Draw a picture to back up your claim.
16