Given: AC = BD Prove: AB = CD. A B C D 2-6 Proving Statements ...
Given: AC = BD Prove: AB = CD. A B C D 2-6 Proving Statements ...
Given: AC = BD Prove: AB = CD. A B C D 2-6 Proving Statements ...
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September 27, 20102-6 <strong>Proving</strong> <strong>Statements</strong> about Segments<strong>Given</strong>: <strong>AC</strong> = <strong>BD</strong><strong>Prove</strong>: <strong>AB</strong> = <strong>CD</strong>.A B C D
September 27, 2010<strong>Given</strong>: <strong>AB</strong> = <strong>CD</strong><strong>Prove</strong>: <strong>AC</strong> = <strong>BD</strong>.A B C D
September 27, 2010theorem: proven statementLinear Pair Theorem: If two angles form a linear pair, thenthey are supplementary.DProof.1 2A B C<strong>Given</strong>: 1 and 2 form a linear pair<strong>Prove</strong>: 1 supp 2<strong>Statements</strong>Reasons1.2.3.4.5.1 and 2 form a linear pair 1.2.3.4.5.given6.1 supp 26.
September 27, 2010A B <strong>CD</strong>
September 27, 2010Congruent Complements Theorem:Congruent Supplements Theorem:
September 27, 20101. <strong>Given</strong>: m 1 = 24, m 3 = 241 comp. 23 comp. 4<strong>Prove</strong>: 2 = 4StatementReason1. __________________ 1. given2. __________________ 2. given3. __________________ 3. ____________________4. 1 = 3 4. ____________________5. __________________ 5. given6. __________________ 6. given7. __________________ 7. _____________________
September 27, 2010Right Angle Congruence Theorem:All right angles are congruent.<strong>AB</strong>2. <strong>Given</strong>: A and<strong>Prove</strong>: A = BStatementB are right anglesReason1. A and B are right angles 1.2. A = 90 ; B = 90 2.3. m A = m B 3.4. 4. Definition of = angles
September 27, 20103. <strong>Given</strong>: D<strong>AB</strong> and <strong>AB</strong>C are rt. angles<strong>AB</strong>C = B<strong>CD</strong><strong>Prove</strong>: D<strong>AB</strong> = B<strong>CD</strong>D<strong>AC</strong>BStatementReason1. _____________________ 1. _____________________2. _____________________ 2. _____________________3. _____________________ 3. _____________________4. <strong>AB</strong>C = B<strong>CD</strong> 4. _____________________5. _____________________ 5. _____________________
September 27, 20104. <strong>Given</strong>: 1 = 2, 3 = 42 = 3B<strong>Prove</strong>: 1 = 4<strong>AC</strong>StatementReason1. ______________________ 1. given2. ______________________ 2. given3. ______________________ 3. ______________________4. 3 = 4 4. given5. ______________________ 5. _______________________
September 27, 20105. <strong>Given</strong>: m 1 = 63, 1 = 33 = 4<strong>Prove</strong>: m 4 = 63StatementReason1. ___________________ 1. given2. ___________________ 2. given3. ___________________ 3. ____________________4. ___________________ 4. defn. = angles5. m 1 = 63 5. given6. ___________________ 6. ________________________
September 27, 20106. <strong>Given</strong>: LK = 5, JK = 5, JK = JLK<strong>Prove</strong>: LK = JLJLStatementReason1. 1. given2. 2. given3. LK = JK 3.4. LK = JK 4.5. JK = JL 5.6. 6.
September 27, 20107. <strong>Given</strong>: X is the midpoint of MNMX = RXMXS<strong>Prove</strong>: XN = RXRNStatementReason1. 1.2. 2. Definition of midpoint3. 3. given4. XN = RX 4.
September 27, 20108. <strong>Given</strong>: RS = XYST = WX<strong>Prove</strong>: RT = WYR S TW X YStatementReason1. 1. given2. 2. given3. 3. Segment Addition Postulate4. XY + WX = RT 4.5. WX + XY = WY 5.6. RT = WY 6.
September 27, 20109. <strong>Given</strong>: <strong>AB</strong> = BC, BC = <strong>CD</strong>Find BC.A3x-1 2x+3DBC
September 27, 201010.<strong>Given</strong>: RT = WX, ST = WX<strong>Prove</strong>: RS = XYR S TW X YStatementReason1. ____________________ 1. given2. RT = WY 2. ____________________3. ____________________ 3. Segment Addition Postulate4. ____________________ 4. Segment Addition Postulate5. ____________________ 5. _____________________6. ST = WX 6. given7. RS = XY 7.8. RS = XY 8. ______________________
September 27, 201011. <strong>Given</strong>: AD = 8, BC = 8, BC = <strong>CD</strong>B<strong>Prove</strong>: AD = <strong>CD</strong>CADStatementReason1. ________________ 1. given2. BC = 8 2. _______________3. ________________ 3. transitive4. ________________ 4. Definition of = segments5. BC = <strong>CD</strong> 5. ____________________6. AD = <strong>CD</strong> 6. _____________________
September 27, 201011. <strong>Given</strong>: AD = 8, BC = 8, BC = <strong>CD</strong>B<strong>Prove</strong>: AD = <strong>CD</strong>CADStatementReason1. ________________ 1. given2. BC = 8 2. _______________3. ________________ 3. transitive4. ________________ 4. Definition of = segments5. BC = <strong>CD</strong> 5. ____________________6. AD = <strong>CD</strong> 6. _____________________
September 27, 201012. <strong>Given</strong>: BC = <strong>CD</strong> , AD = <strong>CD</strong>AD = 12, <strong>AB</strong> = 12B<strong>Prove</strong>: BC = BA<strong>AC</strong>DStatementReason1. BC = <strong>CD</strong> 1. given2. AD = <strong>CD</strong> 2. given3. __________________ 3. transitive4. AD = 12 4. given5. <strong>AB</strong> = 12 5. given6. AD = <strong>AB</strong> 6. ____________________7. AD = <strong>AB</strong> 7. _____________________8. ____________________ 8. transitive
September 27, 201013. Solve for the variable. Explain your steps.<strong>AC</strong> = 91x-10 4x+1A B CStatementReason1. <strong>AC</strong> = 91 1. __________________2. <strong>AB</strong> + BC = <strong>AC</strong> 2. __________________3. x - 10 + 4x + 1 = 91 3. substitution4. 5x - 9 = 91 4. simplify5. __________________ 5. addition6. __________________ 6. ___________________
September 27, 201014. <strong>Given</strong>: EG = HFFind x.Statement4x x+9E F G HReason1. EG = HF 1. __________________2. FG = FG 2. __________________3. EG = HF, FG = FG, 3. ___________________4. EF + FG = EG, 4. ___________________FG + GH = HF5. ___________________ 5. substitution6. ____________________ 6. subtraction7. 7. substitution8. 3x = 9 8. __________________9. x = 3 9. __________________
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