Transitive Property of Equality Variation 2

Distance Property 1

Angle Symmetry Example 2

Collinear Angles Property 9

Transitive Property Application 2

Angles of an Isosceles Triangle

Transitive Property of Equality Variation 3

Angle Symmetry Property 5

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

Exterior Angle Other B

Distance is Greater Than Distance 2

Angle a Greater Than Angle B

Distance Property 4

Angle Symmetry B

Isosceles Triangle Opposites

Distance is Greater Than Distance

Isosceles Triangle Opposites 2

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

Outer Gt Inner

Unequal Angles Theorem

if m∠ZXY > m∠XYZ, then distance ZY > distance ZX

This is a proof by contradiction

Given(s)

m∠ZXY > m∠XYZ

Contradiction 1

Assumption

1	distance ZY = distance ZX

Proof Table

#	Claim	Reason
1	m∠ZXY = m∠XYZ	if distance ZY = distance ZX, then m∠ZXY = m∠XYZ (Isosceles Triangle Opposites)

The last statement (m∠ZXY = m∠XYZ) contradicts a given statement

Contradiction 2

Assumption

1	distance ZY < distance ZX

Proof Table

#	Claim	Reason
1	m∠ZXY < m∠XYZ	if distance ZY < distance ZX, then m∠ZXY < m∠XYZ (Lengths Unequal Then Angles Flipped 2)

The last statement (m∠ZXY < m∠XYZ) contradicts a given statement

Conclusion

distance ZY > distance ZX

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