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

Proof: Alternate Interior Angles Theorem (Converse) 2

Let's prove the following theorem:

if WS || TZ, then m∠WST = m∠STZ

W X Y Z S T

Proof:

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Given
1 WS || TZ
Additional Assumptions
2 m∠WSX = 180
3 m∠YTZ = 180
Proof Table
# Claim Reason
1 WX || YZ if WS || TZ and m∠WSX = 180 and m∠YTZ = 180, then WX || YZ
2 m∠WST = m∠STZ if WX || YZ and m∠WSX = 180 and m∠YTZ = 180, then m∠WST = m∠STZ
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