ALGEBRA & CARTESIAN PLANE



Geometry Unit 1 - Logic and Segments

Vocabulary Terms:

Plane

Point

Ray

Line

Segment

Endpoint

Opposite rays

Postulates

Collinear

Coplanar

Noncollinear

Noncoplanar

Intersection

Inductive reasoning

Conjecture

Analyze

Given information

Patty paper

Midpoint

Congruence

Bisector

Tick Mark

Prove

Postulate

Notation

Compass

Straight Edge

Distance

Length

Construction

Intersection

Conditional

Hypothesis

Conclusion

Inverse

Converse

Contrapositive

Truth Value

Biconditional

Counterexample

Negation

Logically equivalent

p→ q

Deductive Reasoning

Law of Syllogism

Valid deductive argument (conclusion)

|8/26 |8/27 |8/28-29 |8/30 |

|Opening Day |Naming Basic Geometric Structures |Relationships of points, lines, and |QUIZ |

| | |planes | |

|9/2 |9/3 |9/4-5 |9/6 |

|Holiday |Segments |Inductive reasoning/Deductive Reasoning|Conditionals |

|9/9 |9/10 |

|Review |Test |

Tuesday, 8/27

|Chapter 1 Section 1: Understanding Points, Lines, and Planes |

|I can recognize and use the markings used in geometry. |

|I know the differences between Euclidean and Non-Euclidean Geometry |

|ASSIGNMENT: Pg. 9 (#1 – 10, 28, 30, 33-34, 36, 43) 16 problems |Completed: |

Wednesday-Thursday, 8/28-29

|Chapter 1 Section 1: Understanding Points, Lines, and Planes |

|I can use geometric patterns to make valid conjectures. |

|I know the relationships between points, lines, and planes. |

|ASSIGNMENT: Pg. 9 (#11, 12, 20, 21, 25-27, 29, 31-32, 38 – 42, 46) 16 problems |Completed: |

|And “Geometric Structures Model” | |

Friday, 8/30

|Chapter 1 Section 1: Understanding Points, Lines, and Planes |

|I can recognize and use the markings used in geometry. |

|I know the differences between Euclidean and Non-Euclidean Geometry |

|I can use geometric patterns to make valid conjectures. |

|I know the relationships between points, lines, and planes. |

|ASSIGNMENT: Quiz |Completed: |

Tuesday, 9/3

|Chapter 1 Section 2: Measuring and Constructing Segments |

|I can solve problems using Segment Addition Postulate, midpoints, or bisectors. |

|I can recognize the markings used in geometric constructions. |

|I can recognize the markings used in geometric symbolism. |

|ASSIGNMENT: Pg. 17 #1-10, 19, 24-27, 36-39, 44 (20 problems) |Completed: |

Wednesday-Thursday, 9/4-5

|Chapter 2 Section 1: Using Inductive Reasoning to Make Conjectures Chapter 2 Section 3: Using Deductive Reasoning to Verify Conjectures |

|I can use geometric patterns and inductive reasoning to formulate a rule or make generalizations. |

|I can make valid conjectures given information in various forms. |

|I can provide and recognize a valid deductive argument. |

|I can make valid conjectures given information in various forms. |

|ASSIGNMENT: Pg. 77 – 79 #1, 4, 5, 7, 13, 16, 23, 28, 30, 39 (10 questions) and Supplemental Worksheet (5 questions) |

|ASSIGNMENT: Pg. 91 #1, 6-10, 12-13, 15-18, 23, 27 (14 questions) |Completed: |

Friday, 9/6

|Chapter 2 Section 2: Conditional Statements |

|I can write the converse, inverse, and contrapositive. |

|I can determine the validity of a conditional, converse, inverse, or contrapositive and provide a counterexample when it is false. |

|I can tell when statements are logically equivalent. |

|ASSIGNMENT: Pg. 84 #1-4, 9-12, 16-19, 22, 38, 41, 53 (16 questions) |Completed: |

Monday, 9/9

|Review Day |

|ASSIGNMENT: Review for Test IN CLASS |Completed: |

|ASSIGNMENT: Review for Test AT HOME |Completed: |

Tuesday, 9/10

|Test Day |

|Unit 1 Test: Logic and Segments |Grade: |

If you miss the review day, you are still expected to take the test on the test day.

For more help BEFORE the test:

1. Use the indicated chapters in your book

2. Use the book online (it has videos and a homework help section)

3. Use Moodle to find more resources

4. Come to tutoring (with assignment)

Geometry Unit 1 - Logic and Angles

Day 1 - Chapter 1 Section 1: Understanding Points, Lines, and Planes

Objectives:

➢ I can recognize and use the markings used in geometry.

➢ I know the differences between Euclidean and Non-Euclidean Geometry

|Term |Definition |Picture |Notation |

|Plane |has two dimensions. It is represented by | | |

| |a shape that looks like a floor or wall, | | |

| |but it extends without end. | | |

|Point |has no dimension. It is represented by a | | |

| |dot. | | |

|Ray |AB consists of the endpoint A and all | | |

| |points on AB that lie on the same | | |

| |side of A as B. | | |

|Line |has one dimension. It is represented by a| | |

| |line with two arrowheads, but it extends | | |

| |without end. | | |

|Endpoint |is a point at the end of a segment or | | |

| |beginning of a ray. | | |

|Opposite Rays |have a common endpoint and form a line. | | |

|Collinear |are points that lie on the same line. | | |

|Coplanar |are points that lie in the same plane. | | |

|Noncollinear |Two or more geometric figures intersect | | |

| |if they have one or more points in | | |

| |common. The intersection of the figures | | |

| |is the set of points the figures have in | | |

| |common. | | |

|Noncoplanar |Two figures that are not in the same | | |

| |plane | | |

Practice: Pg. 9 (#1 – 10, 28, 30, 33-34, 36, 43) 16 problems

MORE POINTS, LINES, & PLANES

Important facts about points, lines, and planes.

➢ Two points determine a _______________.

➢ Three NON-COLLINEAR points determine a ________________.

➢ Four NON-COPLANAR points determine _____________.

➢ The intersection of two lines is a ________________.

➢ The intersection of a line and a plane is a _______________.

➢ The intersection of two planes is a _________________.

➢ If two points are in a plane, then the line that contains them is _________________________.

EXAMPLE 2

EXAMPLE 3

Plane Activity

Lesson: Points, Lines, & Planes

1. Are points R, H, and F coplanar to plane N? ___________________

Explain.

2. Are points A, B, and D in plane M? ___________________

Explain.

3. Are points A, B, and D in plane N? ___________________

Explain.

4. Are points F, A, R, and T coplanar? ___________________

Explain.

5. Are points F, S, and G coplanar to plane N? ___________________

Explain.

6. Are points F, S, and G coplanar to plane M? ___________________

Explain.

7. Are points F, S, and G coplanar? ___________________

Explain.

8. Are points C, S, and E coplanar? ___________________

Explain.

9. Name 3 points that are coplanar, but not ___________________

coplanar to plane M or plane N?

Explain.

10. Name 4 points coplanar to M. ___________________

Explain.

11. Write 2 questions of yur own using this intersection of planes M and N.

____________________________________________________________________________________________________

____________________________________________________________________________________________________

____________________________________________________________________________________________________

____________________________________________________________________________________________________

Vocabulary- Segment Addition & Bisectors

1) Segment- (line segment) part of a line consisting of two endpoints and all points between them

2) Distance- absolute value of the difference of the points (coordinates). It can also be called length. (Think of number line)

3) Congruence- same length or measure

4) Midpoint- point that bisects, or divides, the segment into two congruent segments.

5) Perpendicular Bisector- a line perpendicular to a segment at the segment’s midpoint.

Segment Addition

If B is between A and C, then AB + BC = AC.

Example:

If AB = 5, BC = 10, find AC.

Solution

-----------------------

N

O

M

L

S

T

R

U

Q

a) Are points S, O, Q, and M coplanar?

Why or why not?

b) Name the intersection of planes LON and NQM:

Explain:

c) Name the intersection of plane LNO and MN.

Explain:

d) Do S and M determine a line? Why or why not?

e) Name the intersection of UO and MN.

Explain:

1.

V

W

Z

Y

X

J

K

U

a) Name three points that determine plane J.

Points:

b) Name a set of collinear points, and a set of non-collinear points.

$%& Collinear: Noncollinear:

c) Name a set of points, other than those in a) that are coplanar.

Points:

HINT: Draw a picture & label.

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