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Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary...

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Page 1: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.
Page 2: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Five-Minute Check (over Lesson 2–4)

NGSSS

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

Page 3: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Over Lesson 2–4

A. A

B. B

A. valid

B. invalid

Determine whether the stated conclusion is valid based on the given information. If not, choose invalid.Given: A and B are supplementary. Conclusion: mA + mB = 180

0%0%

Page 4: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Over Lesson 2–4

A. A

B. B

0%0%

A. valid

B. invalid

Determine whether the stated conclusion is valid based on the given information. If not, choose invalid.Given: Polygon RSTU has 4 sides.Conclusion: Polygon RSTU is a square.

Page 5: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Over Lesson 2–4

A. A

B. B

0%0%

Determine whether the stated conclusion is valid based on the given information. If not, choose invalid.Given: A and B are congruent.Conclusion: ΔABC exists.

A. valid

B. invalid

Page 6: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Over Lesson 2–4

A. A

B. B

0%0%

A. valid

B. invalid

Determine whether the stated conclusion is valid based on the given information. If not, choose invalid.Given: A and B are congruent.Conclusion: A and B are vertical angles.

Page 7: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Over Lesson 2–4

A. A

B. B

0%0%

A. valid

B. invalid

Determine whether the stated conclusion is valid based on the given information. If not, choose invalid.Given: mY in ΔWXY = 90.Conclusion: ΔWXY is a right triangle.

Page 8: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Over Lesson 2–4

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 1

B. 2

C. 3

D. 4

How many points define a plane?

Page 9: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

MA.912.D.6.4 Use methods of direct and indirect proof and determine whether a short proof is logically valid.

MA.912.G.8.1 Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates and theorems.

Also addresses MA.912.G.8.5.

Page 10: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

You used deductive reasoning by applying the Law of Detachment and the Law of Syllogism. (Lesson 2–4)

• Identify and use basic postulates about points, lines, and planes.

• Write paragraph proofs.

Page 11: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

• postulate

• axiom

• proof

• theorem

• deductive argument

• paragraph proof

• informal proof

Page 12: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.
Page 13: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.
Page 14: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Identifying Postulates

ARCHITECTURE Explain how the picture illustrates that the statement is true. Then state the postulate that can be used to show the statement is true.

A. Points F and G lie in plane Q and on line m. Line m lies entirely in plane Q.Answer: Points F and G lie on line m, and the line lies

in plane Q. Postulate 2.5, which states that if two points lie in a plane, the entire line containing that point lies in that plane, shows that this is true.

Page 15: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

ARCHITECTURE Explain how the picture illustrates that the statement is true. Then state the postulate that can be used to show the statement is true.

B. Points A and C determine a line.

Answer: Points A and C lie along an edge, the line that they determine. Postulate 2.1, which says through any two points there is exactly one line, shows that this is true.

Identifying Postulates

Page 16: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. Through any two points there is exactly one line.

B. A line contains at least two points.

C. A plane contains at least two noncollinear points.

D. A plane contains at least three noncollinear points.

ARCHITECTURE Refer to the picture. State the postulate that can be used to show the statement is true.

A. Plane P contains points A, B, and D.

Page 17: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

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.

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.

Page 18: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Analyze Statements Using Postulates

Answer: Always; Postulate 2.5 states that if two points lie in a plane, then the entire line containing those points lies in the plane.

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.

Page 19: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Analyze Statements Using Postulates

Answer: Never; noncollinear points do not lie on the same line by definition.

B. Determine whether the following statement is always, sometimes, or never true. Explain.

contains three noncollinear points.

Page 20: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

A. A

B. B

C. C

A. Determine whether each statement is always, sometimes, or never true.

Plane A and plane B intersect in exactly one point.

A. always

B. sometimes

C. never

A B C

0% 0%0%

Page 21: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

A. A

B. B

C. C

A B C

0% 0%0%

B. Determine whether each 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

Page 22: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.
Page 23: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Write a Paragraph Proof

Given:

Prove: ACD is a plane.

Proof: and must intersect at C because if two lines intersect, then their intersection is exactly one point. Point A is on and point D is on . Points A, C, and D are not collinear. Therefore, ACD is a plane as it contains three points not on the same line.

Page 24: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.
Page 25: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

Proof:

?

Page 26: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. Definition of midpoint

B. Segment Addition Postulate

C. Definition of congruent segments

D. Substitution

Page 27: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.
Page 28: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) NGSSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

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