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
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Angle Symmetry B
Substitution Example 10
Substitute First Term
Triangles Sum to 180
Substitute 2
Associative
Add 6 Numbers
Add Associative 2
Rearrange Sum 6
Rearrange Sum 6 2
Reorder Terms 2
Add Term to Both Sides 2
Substitution 6
Simplify Rearrange Sum 6
Swap B And C
Reorder Terms 3
Sum of Angles in Quadrilateral is 360
Multiplicative Identity 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Multiply 2
Divide Both Sides
Multiplicative Property of Equality Variation 2
Transitive Property of Equality Variation 3
Division is Commutative
Associative Property
Divide Each Side
Reorder Terms 6
Reorder Terms 7
Converse of the Supplementary Angles Theorem
Aia Then Parallel 3
Interior Supplementary Then Parallel
If Angles Congruent Then Parallelogram
Add Terms Twice
Add Substitute Term
Add Three
Add Four
Reduce Addition
If Equiangular Then Rectangle

Proof: Reorder Terms 2

Let's prove the following theorem:

if (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC), then (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB))

A B C D

Proof:

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

Given
1 (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC)
Proof Table
# Claim Reason
1 (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC) = (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB) (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC) = (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB)
2 (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB)) (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB))
3 (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB) if (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC) and (((((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (m∠ACD)) + (m∠CDA)) + (m∠DAC) = (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB), then (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB)
4 (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB)) if (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB) and (((((m∠ABC) + (m∠CDA)) + (m∠BCA)) + (m∠ACD)) + (m∠DAC)) + (m∠CAB) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB)), then (((m∠ABC) + (m∠BCA)) + (m∠CAB)) + (((m∠ACD) + (m∠CDA)) + (m∠DAC)) = (((m∠ABC) + (m∠CDA)) + ((m∠BCA) + (m∠ACD))) + ((m∠DAC) + (m∠CAB))
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