1 / 53

Objective: To use inductive reasoning to make conjectures.

1-1 Patterns and Inductive Reasoning. Objective: To use inductive reasoning to make conjectures. Inductive reasoning – reasoning that is based on a pattern of examples. EX. Conjecture – a conclusion that you reach based on inductive reasoning.(an educated guess).

lilia
Download Presentation

Objective: To use inductive reasoning to make conjectures.

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. 1-1 Patterns and Inductive Reasoning Objective: To use inductive reasoning to make conjectures.

  2. Inductive reasoning – reasoning that is based on a pattern of examples

  3. EX

  4. Conjecture – a conclusion that you reach based on inductive reasoning.(an educated guess)

  5. Counterexample – an example that shows a conjecture is false

  6. Find a pattern for each sequence. Use the pattern to show the next two terms or figures. 1. 3, –6, 18, –72, 360 2. Use the table and inductive reasoning. 3. Find the sum of the first 10 counting numbers. 4. Find the sum of the first 1000 counting numbers. Show that the conjecture is false by finding one counterexample. 5. The sum of two prime numbers is an even number. –2160; 15,120 55 500,500 Sample: 2+3=5, and 5 is not even

  7. Which statement below is true? a. π > 3.2 b. -4 > 3 c. √5 < 3 d. 0.235 > 2.354

  8. 1-2 Points, Lines, and Planes Objectives: To identify and draw models of points, lines and planes. To determine the characteristics of points, lines and planes.

  9. 1-2 Points, Lines, and Planes point – a location. A point has no size. It is represented by a small dot and is named by a capital letter. • C line – a series of points that extends in two opposite directions ex AB “line AB” BA “line BA” or line t

  10. EXa. P, Q and R b.

  11. Collinear- points that lie on the same line Noncollinear – points that are not on the same line

  12. EX In the figure below, name three points that are collinear and three points that are not collinear. Points Y, Z, and W lie on a line, so they are collinear. For example, X, Y, and Z and X, W, and Z form triangles and are not collinear.

  13. plane – a flat surface that extends without end in all directions.

  14. Coplanar – points that lie in the same plane Noncoplanar - points that do not lie in the same plane

  15. EX Name the plane shown in two different ways. You can name a plane using any three or more points on that plane that are not collinear. Some possible names for the plane shown are the following: plane RST plane RSU plane RTU plane STU plane RSTU

  16. 1-3 Postulates Postulate– a statement that is accepted as true Postulate 1-1

  17. Postulate 1-2 Postulate 1-3

  18. EX • D •E •F

  19. EX plane CGA plane GAH plane GCH plane CAH

  20. Postulate 1-4 Plane M and plane C intersect in AP.

  21. EX CD

  22. 1-4 Conditional Statements and Their Converses Objective: To write statements in if-then form and write converses of the statements. Conditional statements – if-then statements Hypotheses – the if part of a conditional Conclusion – the then part of a conditional

  23. Hypothesis: it is Saturday Conclusion: Elisa plays soccer

  24. Hypothesis: two lines intersect Conclusion: their intersection is a point

  25. There are different ways to express a conditional statement. •If you are a member of congress, then you are a US citizen. •All members of Congress are US citizens. •You are a US citizen if you are a member of Congress.

  26. EX Write two other forms of this statement. If points are collinear, then they lie on the same plane. All collinear points lie on the same line. Points lie on the same line if they are collinear. Three noncollinear points determine a plane Three points determine a plane if they are noncollinear.

  27. Converse – exchange the hypothesis and the conclusion EX Write the converse of this statement. If a figure is a triangle, then it has three angles. Conditional: If a figure is a triangle, then it has three angles. Converse: If a figure has three angles, then it is a triangle. If you can get a driver’s license, then you are at least 16 years old.

  28. Statement: It’s OK to buy the wrong lipstick if you buy it in the right place. If-then form: If you buy lipstick in the right place, then it’s OK to buy the wrong lipstick. Converse: If it’s OK to buy the wrong lipstick, then you should buy it in the right place.

  29. 1-6 A Plan for Problem Solving Objective: Use a problem solving plan to solve problems involving perimeter and area.

  30. Perimeter – the distance around a figure P = 15 + 18 +6 + 6 + 9 + 12 = 66 feet

  31. EX P = 2l + 2w P = 2(9) + 2(5) P = 18 + 10 P = 28 m

  32. Area – the number of square units needed to cover its surface

  33. 19.68 m2

  34. 48 ft2

More Related