Sections 2-3, 2-4, and 2-5 If-Then Statements, Law of Syllogism, and Postulates

Objectives Analyze statements in if-then form. Use the law of syllogism. Identify and use basic postulates about points, lines, and planes. Objectives

Common Core State Standards Content Standards G.MG.3 – Apply geometric methods to solve problems. Mathematical Practices 2) Reason abstractly and quantitatively. 3) Construct viable arguments and critique the reasoning of others. Common Core State Standards

Vocabulary (Section 2-3) Conditional Statement: a statement that can be written in if-then form. EX. If Mrs. Schulte is my teacher, then I take Geometry. The hypothesis of a conditional statement is the phrase immediately following the word if. EX. Mrs. Schulte is my teacher. The conclusion of a conditional statement is the phrase immediately following the word then. EX. I take Geometry. Vocabulary (Section 2-3)

Identify the hypothesis and conclusion of each conditional statement Identify the hypothesis and conclusion of each conditional statement. If a polygon has six sides, then it is a hexagon. Example 1 (Section 2-3)

Identify the hypothesis and conclusion of each conditional statement Identify the hypothesis and conclusion of each conditional statement. If the first performance is sold out, then another one will be scheduled. Example 1 (Section 2-3)

Law of Syllogism (Section 2-4)

What statement follows logically from the given statements? If you do not get enough sleep, then you will be tired. If you are tired, then you will not do well on the test. Example 4 (Section 2-4)

What statement follows logically from the given statements? If Jamal finishes his homework, he will go out with his friends. If Jamal goes out with his friends, he will go to the movies. Example 4 (Section 2-4)

Vocabulary (Section 2-5) A postulate or axiom is a statement that is accepted as true without proof. Basic ideas about points, lines, and planes can be stated as postulates. Vocabulary (Section 2-5)

Postulates (Section 2-5)

More Postulates (Section 2-5)

Determine whether each statement is always, sometimes, or never true Determine whether each statement is always, sometimes, or never true. Explain. If plane T contains 𝐸𝐹 and 𝐸𝐹 contains point G, then plane T contains point G. Example 2 (Section 2-5)

Determine whether each statement is always, sometimes, or never true Determine whether each statement is always, sometimes, or never true. Explain. 𝐺𝐻 contains three noncollinear points. Example 2 (Section 2-5)

Determine whether each statement is always, sometimes, or never true Determine whether each statement is always, sometimes, or never true. Explain. Two intersecting lines determine a plane. Example 2 (Section 2-5)

p.111 #1, 3, 19, 21 p.121 #7, 30, 32, 33 p.130 #9, 24, 26-29 Homework