Transitive Property of Equality Variation 2
Right Angle Reverse
Tangent 2
Transitive Property of Equality Variation 1
Divide Both Sides
Divide Both
Divide Distances
Tangent
Tangent 3
Tangent 4
Tangent 5

Proof: Tangent 5

Let's prove the following theorem:

if ∠ABC is a right angle, then tangent of (m∠CAB) = (distance CB) / (distance AB)

Proof:

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Given
1 ∠ABC is a right angle
Proof Table
# Claim Reason
1 tangent of (m∠CAB) = (distance BC) / (distance AB) if ∠ABC is a right angle, then tangent of (m∠CAB) = (distance BC) / (distance AB)
2 distance BC = distance CB distance BC = distance CB
3 (distance BC) / (distance AB) = (distance CB) / (distance AB) if distance BC = distance CB, then (distance BC) / (distance AB) = (distance CB) / (distance AB)
4 tangent of (m∠CAB) = (distance CB) / (distance AB) if tangent of (m∠CAB) = (distance BC) / (distance AB) and (distance BC) / (distance AB) = (distance CB) / (distance AB), then tangent of (m∠CAB) = (distance CB) / (distance AB)
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