Transitive Property of Equality Variation 2
Distance Property 1
Distance Property 2
Distance Property 3
Angle Symmetry Example 2
Collinear Angles Property 9
Transitive Property Application 2
Angles of an Isosceles Triangle
Angle Symmetry Example
Angle Symmetry 2
Isosceles Triangle 2
Transitive Property of Equality Variation 1
Perpendicular to Angle
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
Equality Example
If Two Angles Equal Then Three Angles Equal
Angle Angle Side Triangle
Altitudes Isosceles

Alternate Interior Angles Theorem (Converse)

if WX || YZ and m∠WSX = 180 and m∠YTZ = 180, then m∠WST = m∠STZ

This is a proof by contradiction

Given(s)

  • WX || YZ

Contradiction
Assumption
1 m∠YTZ = 180
Assumptions
2 m∠HST = m∠STZ
3 m∠HSI = 180
4 line HI intersects line WX at point S
Proof Table
# Claim Reason
1 HI || YZ if m∠HSI = 180 and m∠YTZ = 180 and m∠HST = m∠STZ, then HI || YZ
2 line WX intersects line YZ at point X if HI || YZ and line HI intersects line WX at point S, then line WX intersects line YZ at point X
The last statement (line WX intersects line YZ at point X) contradicts a given statement


Conclusion

m∠WST = m∠STZ
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