Upload
nibaw
View
51
Download
4
Embed Size (px)
DESCRIPTION
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 Principles. Unit Essential Question: - PowerPoint PPT Presentation
Citation preview
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