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: Angle Symmetry Example

Let's prove the following theorem:

if m∠ABC = m∠XYZ, then m∠ABC = m∠ZYX

Proof:

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

Given

1	m∠ABC = m∠XYZ

Proof Table

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

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