Transitive Property of Equality Variation 2

Distance Property 1

Distance Property 2

Distance Property 3

Angle Symmetry Example 2

Collinear Angles Property 9

Transitive Property Application 2

Angles of an Isosceles Triangle

Angle Symmetry Example

Angle Symmetry 2

Isosceles Triangle 2

Transitive Property of Equality Variation 1

Perpendicular to Angle

Collinear Then 180

Subtract Both Sides

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

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

Equality Example

If Two Angles Equal Then Three Angles Equal

Angle Angle Side Triangle

Altitudes Isosceles

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)

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) (Interior Property (Converse))
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) (Angle Addition Postulate)

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