Opening 1 is a supplement of 2 and m1 = 32°. Find m2.

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Presentation transcript:

Opening 1 is a supplement of 2 and m1 = 32°. Find m2. 5 is a complement of 6 and m5 = 59°. Find m6. 7 is a supplement of 8 and m7 = 18°. Find m8. Supplement: 180 – 32 = 148° = m2 Supplement: 180 – 155 = 25° = m4 Complement: 90 – 59 = 31° = m6 Supplement: 180 – 18 = 162° = m8

Postulates and Diagrams Lesson 2-3 Postulates and Diagrams

Lesson Outline Opening Objectives Vocabulary Key Concept Examples Summary and Homework

Click the mouse button or press the Space Bar to display the answers. 5-Minute Check on Section 2 What is the type of reasoning that uses examples? What is the type of reasoning that uses facts and theorems? What are the three laws of logic from last section? Use the Venn Diagram to answer the following: How many students were at the JV match? How many students were at the varsity match? How many were at both? How many were at neither? Inductive reasoning Deductive reasoning Laws of Syllogism, Detachment and Contrapositive 6 + 4 = 10 JV Var 6 4 12 Wrestling Attendance 5 4 + 12 = 16 4 5 Click the mouse button or press the Space Bar to display the answers.

Objectives Identify postulates using diagrams Sketch and interpret diagrams

Vocabulary Line perpendicular to a plane – if and only if it is perpendicular to every line in the plane that intersects it

Key Concept Each line contains (at least) two points and lines intersect in a single point.

Key Concept Each plane contains (at least) 3 noncollinear points and two planes intersect in a line

Example 1A State the postulate illustrated by the diagram: If then . Answer: a line contains at least two points

Example 1B State the postulate illustrated by the diagram: If then . Answer: three noncollinear points form exactly one plane

Example 2 Use the diagram to write an example of the Three Point Postulate. Answer: A, B, and C are three noncollinear points lying on only one plane P

Example 3 Sketch a diagram showing 𝑽𝑿 intersecting 𝑼𝑾 at 𝑽 so that 𝑽𝑿 is perpendicular to 𝑼𝑾 and 𝑼, 𝑽, and 𝑾 are collinear. Answer: U W V X

Example 4 Use the diagram. Which statements cannot be assumed from the diagram? There exists a plane that contains points 𝑨, 𝑫, and 𝑬. 𝑨𝑩=𝑩𝑭. Answer: First statement is true; any three noncollinear points make a plane. Second statement cannot be assumed from the diagram.

Summary & Homework Summary: Homework: Postulates are things that we accept to be true Theorems are things that we can prove to be true Homework: none