Five-Minute Check (over Lesson 2–4) Mathematical Practices Then/Now Postulate 2.8: Ruler Postulate Postulate 2.9: Segment Addition Postulate Example 1: Use the Segment Addition Postulate Theorem 2.2: Properties of Segment Congruence Proof: Transitive Property of Congruence Example 2: Real-World Example: Proof Using Segment Congruence Lesson Menu

In the figure shown, A, C, and lie in plane R, and B is on 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? 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. 5-Minute Check 1

In the figure shown, A, C, and lie in plane R, and B is on 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? 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. 5-Minute Check 2

In the figure shown, A, C, and lie in plane R, and B is on 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? 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. 5-Minute Check 3

Determine if the statement is always, sometimes, or never true. Three intersecting lines are in the same plane. A. always B. sometimes C. never D. not enough information 5-Minute Check 4

Which statement shows an example of the Symmetric Property? A. x = x B. If x = 3, then x + 4 = 7. C. If x = 3, then 3 = x. D. If x = 3 and x = y, then y = 3. 5-Minute Check 5

Which statement and reason are missing from the following proof? A. 3x + 3 = 24 + 3; Addition Property B. 3x – 3 = 24 – 3; Subtraction Property C. 3x = 3(24); Multiplication Property D. ; Division Property 5-Minute Check 6

Mathematical Practices 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). MP

You wrote algebraic and two-column proofs. Write proofs involving segment addition. Write proofs involving segment congruence. Then/Now

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2. Definition of congruent segments AB = CD 2. Use the Segment Addition Postulate Proof: Statements Reasons 1. 1. Given AB  CD ___ 2. Definition of congruent segments AB = CD 2. 3. Reflexive Property of Equality BC = BC 3. 4. Segment Addition Postulate AB + BC = AC 4. Example 1

5. Substitution Property of Equality 5. CD + BC = AC Use the Segment Addition Postulate Proof: Statements Reasons 5. Substitution Property of Equality 5. CD + BC = AC 6. Segment Addition Postulate CD + BC = BD 6. 7. Transitive Property of Equality AC = BD 7. 8. Definition of congruent segments 8. AC  BD ___ Example 1

Given: AC = AB AB = BX CY = XD Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD Example 1

Which reason correctly completes the proof? 1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition Property AC + CY = BX + XD 4. AY = BD 6. Substitution 6. Proof: Statements Reasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ? Example 1

C. Definition of congruent segments A. Addition Property B. Substitution C. Definition of congruent segments D. Segment Addition Postulate Example 1

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Proof Using Segment Congruence BADGE Jamie is designing a badge for her club. The length of the top edge of the badge is equal to the length of the left edge of the badge. The top edge of the badge is congruent to the right edge of the badge, and the right edge of the badge is congruent to the bottom edge of the badge. Prove that the bottom edge of the badge is congruent to the left edge of the badge. Given: Prove: Example 2

2. Definition of congruent segments 2. Proof Using Segment Congruence Proof: Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. Given 3. 4. Transitive Property 4. YZ ___ 5. Symmetric Property 5. 6. Substitution 6. Example 2

Prove the following. Given: Prove: Example 2

Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. Given 3. 4. Transitive Property 4. 5. _______________ 5. ? Example 2

C. Segment Addition Postulate A. Substitution B. Symmetric Property C. Segment Addition Postulate D. Reflexive Property Example 2