Concept.

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Presentation transcript:

Concept

Concept

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

What is your plan of attack? Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD What is your plan of attack? Example 1

5. Segment Addition Postulate AC + CY = AY; BX + XD = BD 5. Proof: Statements Reasons 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. 5. Segment Addition Postulate AC + CY = AY; BX + XD = BD 5. AY = BD 6. Substitution 6. Example 1

Concept

Concept

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. Substitution 5. 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

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

End of the Lesson