1. Splash Screen

2. Five-Minute Check (over Lesson 2–4) CCSS Then/Now New Vocabulary
Postulates: Points, Lines, and Planes
Key Concept: Intersections of Lines and Planes
Example 1: Real-World Example: Identifying Postulates
Example 2: Analyze Statements Using Postulates
Key Concept: The Proof Process
Example 3: Write a Paragraph Proof
Theorem 2.1: Midpoint Theorem
Lesson Menu

3. Mathematical Practices 2 Reason abstractly and quantitatively.
Content Standards
G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Mathematical Practices
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
CCSS

4. Identify and use basic postulates about points, lines, and planes.
You used deductive reasoning by applying the Law of Detachment and the Law of Syllogism.
Identify and use basic postulates about points, lines, and planes.
Write paragraph proofs.
Then/Now

5. postulate axiom proof theorem deductive argument paragraph proof
informal proof
Vocabulary

6. Concept

7. Concept

8. Concept

9. Concept

10. Concept

11. Concept

12. Concept

13. ARCHITECTURE Refer to the picture
ARCHITECTURE Refer to the picture. State the postulate that can be used to show the statement is true. A. Plane P contains points E, B, and G.
A. Through any two points there is exactly one line.
B. A line contains at least two points.
C. A plane contains at least three noncollinear points.
D. A plane contains at least two noncollinear points.
Example 1

14. ARCHITECTURE Refer to the picture
ARCHITECTURE Refer to the picture. State the postulate that can be used to show the statement is true. B. Line AB and line BC intersect at point B.
A. Through any two points there is exactly one line.
B. A line contains at least two points.
C. If two lines intersect, then their intersection is exactly one point.
D. If two planes intersect, then their intersection is a line.
Example 1

15. If plane T contains contains point G, then plane T contains point G.
Analyze Statements Using Postulates
A. Determine whether the following statement is always, sometimes, or never true. Explain.
If plane T contains contains point G, then plane T contains point G.
Answer: Always; The Postulate states that if two points lie in a plane, then the entire line containing those points lies in the plane.
Example 2

16. contains three noncollinear points.
Analyze Statements Using Postulates
B. Determine whether the following statement is always, sometimes, or never true. Explain.
contains three noncollinear points.
Answer: Never; noncollinear points do not lie on the same line by definition.
Example 2

17. A. Determine whether the statement is always, sometimes, or never true
A. Determine whether the statement is always, sometimes, or never true. Plane A and plane B intersect in exactly one point.
A. always
B. sometimes
C. never
Example 2

18. B. Determine whether the statement is always, sometimes, or never true
B. Determine whether the statement is always, sometimes, or never true. Point N lies in plane X and point R lies in plane Z. You can draw only one line that contains both points N and R.
A. always
B. sometimes
C. never
Example 2

19. Homework
Pgs
1-9, 10-13, 16-29, 34-41

20. End of the Lesson