Transitive Property of Equality Variation 2

Transitive Property of Equality Variation 3

Distance Property 4

Distance Property 1

Angle Symmetry Example 2

Collinear Angles Property 9

Transitive Property Application 2

Angles of an Isosceles Triangle

Angle Symmetry B

Isosceles Triangle Opposites

Distance is Greater Than Distance

Isosceles Triangle Opposites 2

Distance Property 5

Distance Property 6

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

Collinear Angles Property 10

Angle Addition Theorem

Commutative Property Variation 1

Substitution 2

Substitution 6

Rearrange Angles

Whole is Greater Than Parts

Vertical Angles 3

Collinear Angles Property 3

Collinear Angles Property 3 B

Collinear Angles Property 3 C

Exterior Angle Other

Angle Symmetry 4

Collinear Angles Property 7

Exterior Angle Other C

If Lengths are Unequal Then Angles

Lengths Unequal Then Angles Flipped

Lengths Unequal Then Angles Flipped 2

angles unequal then lengths

Angles Unequal Then Lengths 2

Proof: Distance Property 5

Let's prove the following theorem:

if distance AB = distance CD, then distance DC = distance AB

Proof:

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

Given

1	distance AB = distance CD

Proof Table

#	Claim	Reason
1	distance CD = distance DC	distance CD = distance DC (Distance Equality Property)
2	distance DC = distance AB	if distance AB = distance CD and distance CD = distance DC, then distance DC = distance AB (Transitive Property of Equality Variation 3)

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