1 / 24

Warm Up January 30,2012 Please turn in your worksheets.

Warm Up January 30,2012 Please turn in your worksheets. If ray BD is a bisector of <ABC: a) and m <ABC equals 70 degrees, what is the measure of <BDC? b) and m <ABC equals (x+12) and m <BDC equals (2x-36), what is x?. Do you remember?. Solve the system. y=x+5 y=-x+7.

leyna
Download Presentation

Warm Up January 30,2012 Please turn in your worksheets.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Warm Up January 30,2012Please turn in your worksheets. • If ray BD is a bisector of <ABC: a) and m<ABC equals 70 degrees, what is the measure of <BDC? b) and m<ABC equals (x+12) and m<BDC equals (2x-36), what is x?

  2. Do you remember? • Solve the system. y=x+5 y=-x+7

  3. What were the 10 formulas from last week? • Area of square, parallelogram, triangle, circle, regular polygon, sector, trapezoid • Other Formulas for midpoint, distance • Definition of bisector

  4. January 30,2012Today’s Goals…

  5. Deductive Reasoning • Given a rule, state the example belongs. • Example: Every square is a rectangle. • ABCD is a square so by deductive reasoning ABCD is a rectangle.

  6. Inductive Reasoning • Reasoning that is based on patterns you observe. • If you observe a pattern in a sequence, you can use inductive reasoning to tell what the next term in the sequence will be. • See the examples follow a pattern then write the rule.

  7. a.) 3, 6, 12, 24… Ex.1: Finding and Using a PatternFind a pattern for each sequence. Use the pattern to show the next two terms in the sequence. b.) You Try… c.) 1, 2, 4, 7, 11, 16, 22, … d.)

  8. Conjecture • A conclusion you reach using inductive reasoning. • A good guess • The rule you observe

  9. Do you see the pattern? • State the rule then identify the next two terms. 1) o,t,t,f,f,s,s,e 2) Aquarius, Pisces, Aries, Taurus

  10. Ex.2: Using Inductive ReasoningMake a conjecture about the sum of the first 30 odd numbers. • What do you notice? 1 = 1 + 3 = 1 + 3 + 5 = 1 + 3 + 5 + 7 = • Using inductive reasoning, you can conclude that the sum of the first 30 odd numbers is 302, or 900.

  11. Counterexample • Not all conjectures turn out to be true. • You can prove that a conjecture is false by finding ONE counterexample. • A counterexample to a conjecture is an example for which the conjecture is incorrect.

  12. Ex.3: Testing a ConjectureSome products have 5 as a factor, as shown. • Which conjecture is true? • If false, state a counterexample. • The product of 5 and any odd number is odd. • The product of 5 and any number ends in 5.

  13. The beginning of geometric thought • To start off we have to have some words without a definition. We have an understanding of what they are. • The three words are point, line and plane.

  14. P Point • You can think of a point as a location. • No size • Represented by a small dot • Named by a capital letter • Space is defined as the set of all points.

  15. A B Line • You can think of a line as a series of points that extends in two opposite directions without end. • Name a line two different ways: • Use two points on the line such as AB (read “line AB”) • Use a single lowercase letter such as “line t” • Collinear points are points that lie on the same line.

  16. Planes P A B C Plane P Plane ABC • A plane is a flat surface that has no thickness. • A plane contains many lines and extends without end in the direction of all its lines. • You can name a plane by either a single capital letter or by at least 3 of its noncollinear points. • Points and lines in the same plane are coplanar.

  17. Which points make the plane?

  18. A postulate or axiom is an accepted statement of fact. We believe it is true just because Euclid said so. • The First Three Postulates: • Through any two points there is exactly one line. • If two lines intersect, then they intersect in exactly one point. • If two planes intersect, then they intersect in exactly one line.

  19. A B Segment • Many geometric figures, such as squares and angles, are formed by parts of lines called segments or rays. • A segment is the part of a line consisting of two endpoints and all points between them.

  20. Q R S Ray A B • A ray is the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint. • Opposite rays are two collinear rays with the same endpoint. Opposite rays ALWAYS form a line.

  21. a b Parallel lines are coplanar lines that do not intersect. • These symbols indicate lines a and b are parallel. a || b

  22. Skew lines are noncoplanar; therefore, they are not parallel and do not intersect. AB || EF AB and CG are skew.

  23. Parallel planes are planes that do not intersect. Plane ABCD || Plane GHIJ

  24. Assignment • Page 6 1-6, 8,10, 19-24 • Page 13 2-24E

More Related