Geometry
Chapter 1 Notes
Chapter 1
Reasoning in Geometry
Section 1-1 Inductive Reasoning
Inductive Reasoning =
Conjecture =
Examples:
Make a conjecture from the following information.
1. Eric was driving his friends to school when his car suddenly
stopped two blocks away from school. Why did his car stop?
2. Rayna was preparing toast for breakfast. After a few
minutes the bread popped up but was not toasted. Why
wasn’t the bread toasted?
Page 1
Geometry
Chapter 1 Notes
A conjecture could be true or false. It only takes ______ false
example to show that a conjecture is false. The false example is
called a ________________________.
Examples:
State whether the conjecture is T or F. IF F, give a counterexample.
3. Conjecture: All prime numbers are odd.
4. Conjecture: If n > 1, then n is always less than n.
5. Conjecture: All humans are mammals.
6. Conjecture: The English alphabet has 26 letters.
7.
Conjecture: If it is cloudy, then it is raining.
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Geometry
Chapter 1 Notes
Make a Conjecture.
8. Given: The sum of any two odd numbers.
Conjecture:
9. Given: The intersection of a circle and a line.
Conjecture:
10. Given: Today is December 25th.
Conjecture:
11. Given: DEFG is a square
Conjecture:
Page 3
Geometry
Chapter 1 Notes
Section 1-2
Points, Lines and Planes
Vocabulary:
Point =
Picture:
Naming:
Line =
Picture:
Naming:
Collinear =
Noncollinear =
Plane =
Picture:
Naming:
Coplanar =
Noncoplanar =
Page 4
Geometry
Chapter 1 Notes
Ray =
Picture:
Naming:
Segment =
Picture:
Naming:
Examples:
List all of the possible names for each figure.
1. line
2. plane
T
A
S
n
R
B
C
R
3. segment and ray
P
Q
R
S
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Geometry
Chapter 1 Notes
Example(s): Draw and label a figure for each situation described.
1. Point G lies on
JK .
2. Points D, E and F are collinear, but points G, D, E and F are
noncollinear.
3. line t
4. Plane RST
5. rays BA and BT so that A, B, and T are non-collinear
6. rays BA and BT so that A, B, and T are collinear
Page 6
Geometry
Chapter 1 Notes
Section 1-3
Postulates
Postulates =
The postulates in this section describe how points, lines, and
planes are related.
Two points determine a
Q
unique line.
P
If two distinct lines
intersect, then their
intersection is a point.
Three noncollinear
points determine a
unique plane.
l
m
T
A
B
C
If two distinct planes
intersect, then their
intersection is a line.
Examples:
1. Name all of the different lines that can be drawn through
B
these points.
A
C
D
2. Name the intersection of AB and DA.
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Geometry
Chapter 1 Notes
3. Name all of the planes that are represented in the figure.
E
F
G
D
I
H
J
K
4. Name the intersection of planes DEG and IJF from the figure
above.
Refer to the picture at the right for the following questions.
E
5. Are points E, F, and C collinear?
6. Are points A and F collinear?
F
7. Are points A, C, D
and E coplanar?
N
A
D
B
C
8. How many planes appear in this figure? Name them.
9. Name a plane containing points D and F.
10. Name the planes that intersect in
AE .
11. What do the dotted lines represent in the figure?
Page 8
Geometry
Chapter 1 Notes
Section 1-4
Conditional Statements and Their Converses
If-then statements join two statements based on a condition.
Therefore, an if-then statement is called a ________________.
A conditional statement has two parts.
Hypothesis =
Conclusion =
Ex: If today is Wednesday, then you will have a quiz in Geometry.
Conditional statements can be written in the form
_________________, ______________________
Shorthand
Notation
If ________, then ________. or
Examples:
Write the following statements in if-then form. Then, identify
the hypothesis and conclusion for each conditional statement.
1. An angle of 40o is acute.
2. A piranha eats other fish.
Page 9
Geometry
Chapter 1 Notes
There are different ways to express a conditional statement.
The following statements all have the same meaning.
 If you are a member of Congress, then you are a US citizen.
 All members of Congress are US citizens.
 You are a US citizen if you are a member of Congress.
Examples:
Write two other forms of each statement.
5. If you eat fruits and vegetables, you will be healthy.
6. You’ll win the race if you run the fastest.
7. All people over the age of 18 can serve in the armed forces.
Converse =
Examples:
Write the converse for examples 1-2 from the previous page.
1.
2.
The converse may NOT be ____________.
Page 10
Geometry
Chapter 1 Notes
Negation =
Example: An angle is obtuse.
Negation
Inverse =
Contrapositive =
Example:
Write the inverse and contrapositive of the following statement
“Acute angles have measures less than 90º.”
Conditional statement in if-then form:
Inverse:
Contrapositive:
Summary
Conditional
Converse
Inverse
Contrapositive
Page 11