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EXAMPLE 3

Prove this property of midpoints: If you know that M is the midpoint of AB ,prove that AB is two times AM and AM is one half of AB. GIVEN:. M is the midpoint of AB. a. AB = 2 AM. PROVE:. AM = AB. b. 1. 2. EXAMPLE 3. Use properties of equality. STATEMENT. REASONS. 1. 1.

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EXAMPLE 3

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  1. Prove this property of midpoints: If you know that Mis the midpoint of AB,prove that ABis two times AMand AMis one half of AB. GIVEN: Mis the midpoint of AB. a. AB= 2AM PROVE: AM=AB b. 1 2 EXAMPLE 3 Use properties of equality

  2. STATEMENT REASONS 1. 1. Mis the midpoint of AB. Given AMMB 2. 2. Definition of midpoint AM= MB 3. 3. Definition of congruent segments AM + MB = AB 4. 4. Segment Addition Postulate 5. AM + AM = AB 5. Substitution Property of Equality 1 a. 6. 2AM = AB 6. Distributive Property 2 b. 7. AM=AB 7. Division Property of Equality EXAMPLE 3 Use properties of equality

  3. 4. WHAT IF? Look back at Example 3. What would be different if you were proving that AB = 2 MB and that MB = ABinstead? ANSWER 1 2 In step 5,6, and 7,AM would be replaced by MB for Example 3 GUIDED PRACTICE

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