Transitive Property of Equality Variation 2

Angle Symmetry Example 2

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 3

Proof: Vertical Angles 3

Let's prove the following theorem:

if m∠WPY = 180 and m∠XPZ = 180, then m∠YPX = m∠WPZ

Proof:

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

Given

1	m∠WPY = 180
2	m∠XPZ = 180

Proof Table

#	Claim	Reason
1	m∠YPW = 180	if m∠WPY = 180, then m∠YPW = 180 (Angle Symmetry Example 2)
2	(m∠YPX) + (m∠XPW) = 180	if m∠YPW = 180, then (m∠YPX) + (m∠XPW) = 180 (Collinear Points Theorem)
3	m∠YPX = 180 + ((m∠XPW) ⋅ (-1))	if (m∠YPX) + (m∠XPW) = 180, then m∠YPX = 180 + ((m∠XPW) ⋅ (-1)) (Add Term to Both Sides 6)
4	(m∠XPW) + (m∠WPZ) = 180	if m∠XPZ = 180, then (m∠XPW) + (m∠WPZ) = 180 (Collinear Points Theorem)
5	m∠WPZ = 180 + ((m∠XPW) ⋅ (-1))	if (m∠XPW) + (m∠WPZ) = 180, then m∠WPZ = 180 + ((m∠XPW) ⋅ (-1)) (Add Term to Both Sides 7)
6	m∠YPX = m∠WPZ	if m∠YPX = 180 + ((m∠XPW) ⋅ (-1)) and m∠WPZ = 180 + ((m∠XPW) ⋅ (-1)), then m∠YPX = m∠WPZ (Transitive Property of Equality Variation 1)

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