Please fill out your student information sheet. Informal Geometry A Mr. L. Lawson

Agenda Session 1 Call Roll & Info Sheets (take up course verification forms) Introductions Class policies & procedures –Syllabus –Pacing guide Assignment #1 Notes (1.1 & 1.2) Assign HW

Worksheet 1.1 & 1.2 Make sure you put your name on your paper. Work quietly by yourself. Complete all that you can Hang on to it if you finish before we begin notes

Informal Geometry A Session 1

(notes)

Inductive Reasoning Making a conclusion based on a pattern of examples or past events. We will look at patterns with numbers and shapes. Goal 1: Find and describe patterns

Example 1: Find the next 3 terms of the sequence. 33, 39, 45, … I’ll look at adding or subtracting the numbers 1 st. Answer: 51, 57, 63 (add 6)

Example 2: Find the next figure in the pattern. Look at the colors and that dot. Answer:

* Look for a Pattern * Make a Conjecture based on your observations * Verify the Conjecture using logical reasoning Goal 2: Use Inductive Reasoning

Conjecture A conclusion that you reach based on observations (a pattern). Conjecture is like an educated guess. For example, if a number of dark clouds cover the sky and the wind picks up, one might conjecture that … It might rain

Conjecture Example 3: Complete the Conjecture: The sum of the first n odd positive integers is ___________. First odd positive integer: 1 Sum first two odd pos int: = 4 Sum first three odd pos int: = 9 Sum first four odd pos int: = 16 Look for a pattern

Conjecture Example 3: Complete the Conjecture: The sum of the first n odd positive integers is ___________. First odd positive integer: 1 Sum first two odd pos int: 1+3 = 4 Sum first three odd pos int: 1+3+5=9 Sum first four odd pos int: =16 =1 2 =2 2 =3 2 =4 2 n two three four n2n2

Conjecture An important part of a conjecture is that they are NOT always correct. For example, after losing a lot of money in the slot machines, a person is likely to say, "I will win the next time".... unfortunately this conjecture is usually wrong.

Counterexample It only takes 1 false example to show that a conjecture is not true. Example 4: Find a counterexample for these statements… All dogs have spots. All prime numbers are odd.

Point Has no size, no dimension Is represented by a dot Named by using a capital letter We would call this one “point E.”

Has one dimension Is made up of infinite number of points and is straight Arrows show that the line extends without end in both directions Can be named with a single lowercase cursive letter OR by any 2 points on the line Symbol Line Names of these lines:

COLLINEAR Points lie on the same line NONCOLLINEAR Points do NOT lie on the same line

Example Points D, B, & C are in a straight line so they are _______________ Points A, B, & C are ________________ A B C D E

2 dimensions Extends without end in all directions Takes at least 3 noncollinear pts. to make a plane Named with a single uppercase script letter or by 3 noncollinear pts. Plane Names of these planes: M

COPLANAR Points lie in the same plane NONCOPLANAR Points do NOT lie in the same plane

Is straight and made up of points Has a definite beginning and definite end Name a line segment by using the endpoints only You will always use two letters to name a segment Symbol Line Segment Name of these segments: A B C D E F G H Name of segment from 3 to 0.

Is straight and made up of points Has a beginning but no end Starting pt. of a ray is called the endpoint Name a ray by using the endpt. 1st and another point on the ray You will always use two letters to name a ray Symbol Ray Names of these rays:

Made up of two rays with a common endpoint The point is called the vertex of the angle The rays are called the sides of the angle Symbol  Several ways to name an angle Angles Names:

Homework Finish the Worksheet!

Journal (session 1) Think of a teacher you have had in the past that was a very good teacher. Describe your ideal math teacher. Do not turn this in today. Keep it with you and put it in your notebook.