Transitive Property of Equality Variation 2

Right Angle Reverse

Proof: Cosine 2a

Let's prove the following theorem:

if ∠ABC is a right angle, then cosine of (m∠CAB) = (distance BA) / (distance AC)

Proof:

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

Given

1	∠ABC is a right angle

Proof Table

#	Claim	Reason
1	cosine of (m∠CAB) = (distance BA) / (distance CA)	if ∠ABC is a right angle, then cosine of (m∠CAB) = (distance BA) / (distance CA) (Cosine 2)
2	distance CA = distance AC	distance CA = distance AC (Distance Equality Property)
3	(distance BA) / (distance CA) = (distance BA) / (distance AC)	if distance CA = distance AC, then (distance BA) / (distance CA) = (distance BA) / (distance AC) (Divide Property)
4	cosine of (m∠CAB) = (distance BA) / (distance AC)	if cosine of (m∠CAB) = (distance BA) / (distance CA) and (distance BA) / (distance CA) = (distance BA) / (distance AC), then cosine of (m∠CAB) = (distance BA) / (distance AC) (Transitive Property of Equality)

Previous Lesson

Comments

Please log in to add comments