Transitive Property of Equality Variation 2
Angle Symmetry Example 2
Distance Property 2
Distance Property 1
Collinear Then 180
Subtract Both Sides
Add Term to Both Sides 6
Subtract Both Sides 2
Add Term to Both Sides 7
Transitive Property of Equality Variation 1
Vertical Angles
Angle Addition Theorem
Collinear Angles Property 9
Collinear Angles B
Exterior Angle
Exterior Angle B
Collinear Angles Property 10
Collinear Angles Property 3
Collinear Angles Property 3 B
Collinear Angles Property 3 C
alternate interior angles then parallel
ParallelThenAIA
Parallelthenaiashort
Parallel Then Aia Short Mirror
Angle Symmetry 4
Angle Symmetry Example
If Parallelogram Diagonal Then Congruent Triangles
If Parallelogram Then Sides Congruent B
If Parallelogram Then Sides Congruent B2
Square is Equilateral
If Parallelogram Then Sides Congruent
Transitive Property of Equality Variation 3
Distance Property 5
Square is Equilateral 2
Square is Equilateral 3
Distance Property 6
Congruent Triangles to Angles
Aiathenparallelshort
Congruent Triangles to Angles 2
Parallel Then Parallelogram
If Sides Congruent Then Parallelogram
If Sides Congruent Then Parallelogram 2
If Sides Congruent Then Parallelogram 3
If Equilateral Then Rhombus
Square is Rhombus
Parallel Then Aia Short Mirror 3
Equal Angles
Angle Symmetry 2
Angle Symmetry 3
Parallel Then Aia Short 3
Angle Symmetry Property 5
Triangles Inside Rhombus
Sides of Rhombus Congruent 4
Equal Angles 2
Diagonal Bisects Rhombus 2
Parallel Then Aia 2
Converse of the Supplementary Angles Theorem
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Substitution Example 10
Supplementary Then 180
Parallel Then Interior Supplementary
Paralleltheninteriorshort
Subtraction Example 2
Add Number to Both Sides
Add Number to Both Sides 2
Rectangle Right Angles 2
Angle Addition Theorem 2
Substitute 2
Multiplicative Identity 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Double
Divide Both Sides
Multiplicative Property of Equality Variation 2
Division is Commutative
Associative Property
Divide Each Side
Reduce Addition 2
Square Example 2

Proof: Double

Let's prove the following theorem:

if a + a = b, then a ⋅ 2 = b

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 a + a = b
Proof Table
# Claim Reason
1 a + a = a ⋅ 2 a + a = a ⋅ 2
2 a ⋅ 2 = b if a + a = a ⋅ 2 and a + a = b, then a ⋅ 2 = b
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