Proof: Complementary Angles

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(m∠AXB) + (m∠BXC) = 90	if ∠AXB and ∠BXC are complementary, then (m∠AXB) + (m∠BXC) = 90 (Complementary Angles)
2	(m∠BXC) + (m∠CXD) = 90	if ∠BXC and ∠CXD are complementary, then (m∠BXC) + (m∠CXD) = 90 (Complementary Angles)
3	m∠AXB = 90 + ((m∠BXC) ⋅ (-1))	if (m∠AXB) + (m∠BXC) = 90, then m∠AXB = 90 + ((m∠BXC) ⋅ (-1)) (Add Term to Both Sides 6)
4	m∠CXD = 90 + ((m∠BXC) ⋅ (-1))	if (m∠BXC) + (m∠CXD) = 90, then m∠CXD = 90 + ((m∠BXC) ⋅ (-1)) (Add Term to Both Sides 7)
5	m∠AXB = m∠CXD	if m∠AXB = 90 + ((m∠BXC) ⋅ (-1)) and m∠CXD = 90 + ((m∠BXC) ⋅ (-1)), then m∠AXB = m∠CXD (Transitive Property of Equality Variation 1)

Comments

Please log in to add comments