Algebraic & Geometric Proofs

Page 1

Statements Reasons

1) 5x-4 = 6 1) Given

2) 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

2

2) 3x+5 = 7 2) Multiplication

2 ·2 ·2

3) 3x = 9 3) Substitution

4) 3x = 9 4) Division

3 3

5) x = 3 5) Substitution

Statements Reasons

1) 2x-7 = 1/3x-2 1) Given

2) 3(2x-7) = 3(1/3x-2) 2) Multiplication

3) 6x-21 = x+6 3) Distribution

4) 5x-21= -6 4) Substitution

5) 5x-21 = -6 5) Addition

+21 +21

6) 5x = 15 6) Division

5 5

7) x = 3 7) Substitution

Given: 2x-7 = 1/3x-2

Prove: x=3

Given: AC=BD

Prove: AB=CD

Statements Reasons

1) AC = BD 1) Given

2) AB + BC = AC 2) Segment Addition

3) BC + CD = BD 3) Substitution

4) AB + BC = BC+ CD 4) Substitution

5) BC ≅ BC 5) Reflexive Property

Statements Reasons

1) AB ≅ CD; C is midpoint of BD 1) Given

2) BC ≅ CD 2) Definition of Midpoint

3) ≅ 3) Definition Perpendicular are right angles Lines

4) ≅ D 4) Right Angle Congruency

5) ΔABC ≅ ΔEDC 5) SAS Congruency

Given: AB ≅ CD; C is the midpoint of BD; AB ┴ BD; ED ┴ BD

Prove: ΔABC ≅ ΔEDC

https://www.youtube.com/watch?v=pZZADeU3khw (Embed)

Algebraic Proofs

Segment Proofs (+ & -)

Triangle Proofs