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Lesson Menu Five-Minute Check (over Lesson 2–5) CCSS Then/Now New Vocabulary Key Concept: Properties of Real Numbers Example 1:Justify Each Step When Solving an Equation Example 2:Real-World Example: Write an Algebraic Proof Example 3:Write a Geometric Proof

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Over Lesson 2–5 5-Minute Check 1 A.A line contains at least two points. B.A line contains only two points. C.A line contains at least three points. D.A line contains only three points. In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show that A, B, and C are collinear?

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Over Lesson 2–5 5-Minute Check 2 A.Through two points, there is exactly one line in a plane. B.Any plane contains an infinite number of lines. C.Through any two points on the same line, there is exactly one plane. D.If two points lie in a plane, then the entire line containing those points lies in that plane. In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show that lies in plane R?

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Over Lesson 2–5 5-Minute Check 3 A.Through any two points on the same line, there is exactly one plane. B.Through any three points not on the same line, there is exactly one plane. C.If two points lie in a plane, then the entire line containing those points lies in that plane. D.If two lines intersect, then their intersection lies in exactly one plane. In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show that A, H, and D are coplanar?

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Over Lesson 2–5 5-Minute Check 4 A.Through any two points, there is exactly one line. B.A line contains only two points. C.If two points lie in a plane, then the entire line containing those points lies in that plane. D.Through any two points, there are many lines. In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show that E and F are collinear?

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Over Lesson 2–5 5-Minute Check 5 A.The intersection point of two lines lies on a third line, not in the same plane. B.If two lines intersect, then their intersection point lies in the same plane. C.The intersection of two lines does not lie in the same plane. D.If two lines intersect, then their intersection is exactly one point. In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show that intersects at point B?

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Over Lesson 2–5 5-Minute Check 6 Which of the following numbers is an example of an irrational number? A.–7 B. C. D.34

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Then/Now You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties of equality to write geometric proofs.

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Vocabulary algebraic proof two-column proof formal proof

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Concept

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Example 1 Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92.

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Example 1 A.a = 12 B.a = –37 C.a = –7 D.a = 7 Solve –3(a + 3) + 5(3 – a) = –50.

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Example 2 Write an Algebraic Proof

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Example 3 Write a Geometric Proof If A B, m B = 2m C, and m C = 45, then m A = 90. Write a two-column proof to verify this conjecture.

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Example 3

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Assignment: 139/ 1-20,42-48,50-58

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