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Statements Reasons 1) 5x-4 = 6 1) Given2) 5x-4 = 6 2) Addition +4 +4 3) 5x = 10 3) Division 5 5 4) x = 2 4) Substitution
Given: 5x-4 = 6 Proof: x = 2
Given: 3x+5 = 7 2 Prove: x = 3
Difficulty: EASY
Difficulty: MEDIUM
Difficulty: MEDIUM
Statements Reasons 1) 3x+5 = 7 1) Given 22) 3x+5 = 7 2) Multiplication 2 ·2 ·2 3) 3x = 9 3) Substitution4) 3x = 9 4) Division 3 3 5) x = 3 5) Substitution
Statements Reasons 1) 2x-7 = 1/3x-2 1) Given2) 3(2x-7) = 3(1/3x-2) 2) Multiplication3) 6x-21 = x+6 3) Distribution4) 5x-21= -6 4) Substitution5) 5x-21 = -6 5) Addition +21 +216) 5x = 15 6) Division 5 5 7) x = 3 7) Substitution
Given: 2x-7 = 1/3x-2Prove: x=3
Given: AC=BDProve: AB=CD
Statements Reasons 1) AC = BD 1) Given2) AB + BC = AC 2) Segment Addition 3) BC + CD = BD 3) Substitution 4) AB + BC = BC+ CD 4) Substitution5) BC ≅ BC 5) Reflexive Property
Statements Reasons 1) AB ≅ CD; C is midpoint of BD 1) Given2) BC ≅ CD 2) Definition of Midpoint3) ≅ 3) Definition Perpendicular are right angles Lines4) ≅ D 4) Right Angle Congruency5) ΔABC ≅ ΔEDC 5) SAS Congruency
Given: AB ≅ CD; C is the midpoint of BD; AB ┴ BD; ED ┴ BDProve: ΔABC ≅ ΔEDC
Algebraic Proofs
Segment Proofs (+ & -)
Triangle Proofs
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