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) (Tangent 4)
2	distance BC = distance CB	distance BC = distance CB (Distance Equality Property)
3	(distance BC) / (distance AB) = (distance CB) / (distance AB)	if distance BC = distance CB, then (distance BC) / (distance AB) = (distance CB) / (distance AB) (Divide Both Sides)
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) (Transitive Property of Equality)

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