Geometry Lesson 1.4A Thurday, August 20, 2015
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1 Geometry: Module 1 Lesson 4 Bellwork: Angle measures and angle bisectors Explain 1: 1) Discuss some random (but necessary) theorems and postulates 2) Understand Conditional Statements 3) Understand difference between inductive and deductive reasoning 4) Be able to use a counterexample to prove false with inductive reasoning Practice: Section 1.4/ 1 8all, 13 16all, 21 26all, 28 Opening 2: 5) Be able to use deductive reasoning to set up and solve equations and justify steps Practice 2: Lesson 1.4/ 17 20all Presentations: Closing:
2 Some Extra Random Definitions and Postulates complementary angles: pg. 48 Linear Pair Theorem: 3 4
3 Postulates about Points, Lines and Planes pg. 50
4 Intersection of Planes Postulates about Points, Lines and Planes pg. 50
5 Postulates about Points, Lines and Planes pg. 51
6 Postulates about Points, Lines and Planes pg. 51
7
8 Example 1) Identify the hypothesis and conclusion of each conditional statement. a) If today is thursday then yesterday was wednesday. b) If an angle is acute, then the angle is less than 90 o. c) To do well in this class you have to study.
9 Writing Conditional statements If you want to do well in this class, then you have to study. Other Ways to Say the Same Thing You will do well in this class if you study. Doing well in this class depends on you studying. To do well in this class you will have to study.
10 Examples of Conditional Statements) pg. 48 (linear pairs are supplementary) pg. 7 pg. 22
11 Examples of Conditional Statements) (If you have two points, then there is always exactly 1 line between them)
12 Example 2) Write each as a conditional statement. a) Obtuse angles are bigger than 90 o. b) All squares are rectangles. c) The sum of two supplementary <'s is 180 o.
13 ex) 1, 2, 4, 8 ex) 1, 2, 3,...
14 If you add 3 consecutive counting numbers... then the sum is always divisible by 3??? Inductive Reasoning: Deductive Reasoning:
15
16 Example 3) Determine if each conditional statement is true. If it's false, provide a counterexample. a) If two angles are supplementary, then they are a linear pair. b) If two angles are acute, then their sum is less than 180 o. c) If you divide an integer by another integer, the result is an integer.
17 Break?
18 Definitions, postulates and theorems to use today. pg. 7 pg. 48 Definition of Midpoint: A point that divides a segment into two equal segments. pg. 10 pg. 22 Definition of Complementary Angles: Two angles whose sum is 90 o. Added Notes Lesson 1.4 Definition of Supplementary Angles: Definition of Angle Bisector: A ray (or segment) that divides an angle into two equal angles. pg. 22 Two angles whose sum is 180 o. pg. 48
19 Example 4) Use deductive reasoning to: 1) state the definition, postulate or theorem you used to set up an equation and 2) Solve the equation to find x. a) Point A is between points M and T on a line. If AM = 2x 1, AT = 3x + 6, and MT = 11x 19, find x
20 Example 4) Use deductive reasoning to: 1) state the definition, postulate or theorem you used to set up an equation and 2) Solve the equation to find x. b) XV is an angle bisector of <SXT. If m<sxv = 5x + 17 and m<sxt = 82, find x.
21 Geometry: Module 1 Lesson 4 Bellwork: Angle measures and angle bisectors Explain 1: 1) Understand difference between inductive and deductive reasoning 2) Be able to use a counterexample to prove false with inductive reasoning 3) Be able to use deductive reasoning to prove statements true Practice: Section 1.4/ 1 8all, 13 26all, 28 Presentations: Meausuring and Constructing Angles: Handout Closing:
22 Section 1.4 F14
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