Transitive Property of Equality Variation 2

Angle Symmetry Example 2

Collinear Angles Property 10

Collinear Angles Property 3

Collinear Angles Property 3 B

Collinear Then Equal

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 3 C

alternate interior angles then parallel

ParallelThenAIA

Parallel Then Aia 2

Vertical Angles C

Parallel Then Corresponding

Parallel Then Corresponding 2

Parallel Then Corresponding Short

Angle Symmetry Example

Angle Symmetry 2

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

Distance Property 3

Congruent Triangles to Distance

Two Angles Equal Then Isosceles

Two Angles Equal Then Isosceles 2

Parallel Then Parallelogram

Parallel Then Aia Short Mirror

Angle Symmetry 4

If Parallelogram Diagonal Then Congruent Triangles

If Parallelogram Then Sides Congruent

If Angles Congruent Trapezoid Isosceles

Proof: Angle Symmetry B

Let's prove the following theorem:

if m∠ABC = m∠XYZ, then m∠CBA = m∠XYZ

Proof:

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

Given

1	m∠ABC = m∠XYZ

Proof Table

#	Claim	Reason
1	m∠ABC = m∠CBA	m∠ABC = m∠CBA (Angle Symmetry Property)
2	m∠CBA = m∠XYZ	if m∠ABC = m∠CBA and m∠ABC = m∠XYZ, then m∠CBA = m∠XYZ (Transitive Property of Equality Variation 2)

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