SKATEBOARD SALES

About how many skateboards will the shop sell in June?

What do you estimate for sales in July? August?

Are you comfortable making a guess about next December?

TERMINOLOGY & BASIC PRINCIPLESUnit Essential Question:

How do you identify the basic notations, definitions, properties, and postulates of geometry?

Geometry

WHAT IS GEOMETRY?

PATTERNSEssential Question:How do you use inductive reasoning?

CONTINUE THE PATTERNS:

1, 3, 5, …

5, 11, 18, 26, …

1, 4, 9, 16, …

Monday, Tuesday, Wednesday, …

VOCABULARY

Inductive Reasoning – Reasoning based on patterns that you observe.

Conjecture – A conclusion you reach based on inductive reasoning.

Counterexample – An example for which the conjecture is incorrect.

MAKE A CONJECTURE

What is the sum of the first 30 odd numbers? (Hint: Look for a pattern)

CONJECTURE

What is the sum of the first 20 even numbers?

Conjecture: 202

COME UP WITH COUNTEREXAMPLES:

Boys are smarter than girls.

Every prime number is odd.

The square of a number is greater than the number.

You can connect three points to form a triangle.

Every rectangle is a square.

THINK, PAIR, SHARE:

What is the goal of using inductive reasoning?

How does inductive reasoning work?

PATTERNS:

WHAT DO YOU THINK?

If you have two points, how many lines can you draw through them?

If two lines intersect, what is their intersection?

If two planes intersect, what is their intersection?

POINTS, LINES, & PLANESEssential Questions:

What are the basic terms in Geometry?

POINTS

Point (undefined) – Name with the capital letter used to label the

point.

LINES- Line (undefined) – Name with any two points

on the line, or with a single lower case letter: AB, n

Collinear – Points that lie on the same line.

PLANES

Name the plane for the front of the ice cube, using 3 non-collinear points.

Plane (undefined) – Plane P, Plane ABC, …

Coplanar – Points that lie on the same plane.

POSTULATES

Postulate or Axiom – A statement taken as fact.

If you have 2 points, how many lines can you draw through them?

Postulate 1-1: Through any two points there is exactly one line.

INTERSECTION OF TWO LINES

If two lines cross, what do they have in common?

Postulate 1-2: If two lines intersect, then their intersection is exactly one point.

INTERSECTION OF TWO PLANES

If two planes cross, what is their intersection?

Postulate 1-3: If two planes intersect, then their intersection is exactly one line.

WOBBLY CHAIRS

Why do chairs sometimes wobble?

Why doesn’t a tripod wobble?

Postulate 1-4: Three noncollinear points determine exactly one plane.

How many planes contain the same 3 collinear points?

PLANES:

Are A, B, G, and H coplanar? If so, shade the plane.

Are B, D, H, and E coplanar? If so, shade the plane.

How many planes contain X, S, and Y?

What is the intersection of Plane VSY and Plane ZYC?

GIVE AN EXAMPLE OF:

Two intersecting Lines:

A Line intersecting a Plane:

Two intersecting Planes:

Two planes that do not intersect:

POINTS, LINES, PLANES, & PROBABILITY

TEXTBOOK WEBSITE

Go to: http://www.phschool.com/math

/

Textbook Companion Sites

Click on High School Math (2007)

Click on Geometry Site

Video Tutorials, Practice Quizzes

SEGMENTS, RAYS, & PARALLEL LINES

Essential Question:What are segments, rays, and parallel lines?

VOCABULARY Segment – the part of a line

consisting of endpoints and the points between them.

Ray – The part of a line consisting of an endpoint and all the points on one side.

Opposite Rays – Two distinct collinear rays with the same endpoint.

NAMING SEGMENTS & RAYS

Name all the segments:

Name all the rays:

Name all the opposite rays:

LINES THAT DO NOT INTERSECT

What do you call lines that do not intersect?

Parallel – Coplanar lines that do not intersect.

Skew – Noncoplanar lines.

When are segments and rays parallel or skew?

Parallel Planes – Planes that do not intersect.

PARALLEL & SKEW

Name all segments parallel to GJ.

Name all segments skew to GJ.

Name a line parallel to Plane ABC.

Name a pair of parallel planes.

THINK, PAIR, SHARE

CREATE A SEGMENT

Create a Segment that is 4 Inches long:

MEASURING SEGMENTSEssential Question:How do you find the length of a segment?

RULER POSTULATE Ruler Postulate – The points of a line can be put into

a one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference between their corresponding numbers.

Huh?

CONGRUENCE

EXAMPLE

If A = -3, B = -1, C = 2, D = 4, and E = 5 Is ? Why or why not?

Compare AB, BC, and AC. What do you see?

DBCA

SEGMENT ADDITION POSTULATE

Why collinear?

Why is B between?

What if there are different letters?

ALGEBRA EXAMPLE

MIDPOINT

Where do you think that a midpoint would be located on a segment?

What might make a good definition?

Midpoint – A point on a segment that divides it into two congruent segments.

A B

EXAMPLE

COMPARE & CONTRAST

Similarities Differences

Segment Addition Postulate & Midpoints

WORD SPLASH

ANGLE

MEASURING ANGLESEssential Question:

How do you find the measure of an angle?

WHAT IS AN ANGLE?

Angle – Two rays with the same endpoint.

Sides

Vertex

HOW DO YOU NAME AN ANGLE?

EXAMPLE

Is it safe to name either angle ? E

What does this mean?

Try and create a 73º angle.

ANGLE CLASSIFICATIONS

Acute

Right

Obtuse

Straight

PRACTICE

CONGRUENT ANGLES

When are Angles Congruent?

Is it the length of their sides?

Is it the angle of their openings?

ANGLE ADDITION POSTULATE

PRACTICE ANGLE ADDITION

ANGLE PAIRS

Vertical Angles – Two angles whose sides are opposite rays.

Adjacent Angles – Two coplanar angles with a common side, a common vertex, and no interior points in common.

ANGLE PAIRS

Complementary Angles – Two angles whose sum is 90º.

Supplementary Angles - Two angles whose sum is 180º.

PRACTICE

Find examples of the following Pairs:

Complementary:

Supplementary:

Vertical:

ASSUMPTIONS FROM THE PICTURE

Adjacent Angles

Adjacent Supplementary

Vertical Angles

Congruent Angles or Segments

Right Angles

Parallel or Perpendicular lines

CAN Assume CANNOT Assume

WHAT CAN YOU CONCLUDE?

CAN YOU MAKE THESE CONCLUSIONS?

SUMMARIZE

Naming Angles

Measuring & Adding Angles

Angle Pairs

Assumptions from Pictures