Proof: Collinear And One Angle is 90
Let's prove the following theorem:
if m∠ABC = 180 and m∠XBA = 90, then m∠XBC = 90
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | ∠ABX and ∠XBC are supplementary | if m∠ABC = 180, then ∠ABX and ∠XBC are supplementary |
2 | (m∠ABX) + (m∠XBC) = 180 | if ∠ABX and ∠XBC are supplementary, then (m∠ABX) + (m∠XBC) = 180 |
3 | m∠XBA = m∠ABX | m∠XBA = m∠ABX |
4 | m∠ABX = 90 | if m∠XBA = m∠ABX and m∠XBA = 90, then m∠ABX = 90 |
5 | 90 + (m∠XBC) = 180 | if (m∠ABX) + (m∠XBC) = 180 and m∠ABX = 90, then 90 + (m∠XBC) = 180 |
6 | m∠XBC = 90 | if 90 + (m∠XBC) = 180, then m∠XBC = 90 |
Comments
Please log in to add comments