Transitive Property of Equality Variation 2
Right Angle Reverse
Collinear Then 180
Converse of the Supplementary Angles Theorem
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Subtract Both Sides
Subtraction Example 2
Add Number to Both Sides
Add Number to Both Sides 2
Angle Symmetry Example 2
Transitive Property of Equality Variation 1
Distance Property 1
Distance Property 2
Distance Property 3
Congruent Triangles to Distance 3
Collinear Angles Property 9
Transitive Property Application 2
Angles of an Isosceles Triangle
Angle Symmetry Example
Angle Symmetry 2
Isosceles Triangle B
Collinear Angles Property 10
Collinear Angles Property 3
Collinear Angles Property 3 B
Collinear Angles Property 3 C
Propagated Transitive Property 3
Add Term to Both Sides 6
Subtract Both Sides 2
Add Term to Both Sides 7
Vertical Angles
Angle Addition Theorem
Collinear Angles B
Exterior Angle
Exterior Angle B
alternate interior angles then parallel
ParallelThenAIA
Parallelthenaiashort
Angle Symmetry B
Substitution Example 10
Substitute First Term
Triangles Sum to 180
Equality Example
If Two Angles Equal Then Three Angles Equal
Angle Angle Side Triangle
Angle Angle Side Triangle 2
Congruent Triangle Transitive Property
Hypotenuse And Leg Then Right Triangle Congruent
Bisector Angle

Proof: Angle Addition Theorem

Let's prove the following theorem:

if point X lies in interior of ∠ABC, then m∠ABC = (m∠ABX) + (m∠XBC)

A C B X

Proof:

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

Given
1 point X lies in interior of ∠ABC
Proof Table
# Claim Reason
1 ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180) if point X lies in interior of ∠ABC, then ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180)
2 m∠ABC = (m∠ABX) + (m∠XBC) if ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180), then m∠ABC = (m∠ABX) + (m∠XBC)
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