Transitive Property of Equality Variation 2
Sides of an Equilateral Triangle
Sides of an Equilateral Triangle 2
Distance Property 1
Angle Symmetry Example 2
Collinear Angles Property 9
Transitive Property Application 2
Angles of an Isosceles Triangle
Angles of an Isosceles Triangle 5
Angles of an Equilateral Triangle
Distance Property 2
Transitive Property of Equality Variation 3
Angle Symmetry Property 5
Angles of an Isosceles Triangle 4
Angles of an Isosceles Triangle 4 A
Angles of an Equilateral Triangle 2
Angles of an Equilateral Triangle 3
Transitive Property of Equality Variation 1
Propagated Transitive Property 3
Angles of an Equilateral Triangle 4
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
Substitute 2
Add Term to Both Sides 2
Multiplicative Identity 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Add Three
Divide Both Sides
Multiplicative Property of Equality Variation 2
Division is Commutative
Associative Property
Divide Each Side
Equilateral Triangle 60
Angles of an Equilateral Triangle 5
Angles of an Equilateral Triangle 6
Equilateral Triangle 60 2

Proof: Propagated Transitive Property 3

Let's prove the following theorem:

if the following are true:
  • a = x
  • b = y
  • x = y

then a = b

Proof:

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

Given
1 a = x
2 b = y
3 x = y
Proof Table
# Claim Reason
1 a = y if a = x and x = y, then a = y
2 a = b if a = y and b = y, then a = b
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