Proof: Bisector SAS 2
Let's prove the following theorem:
if ray BX bisects ∠ABC and distance AB = distance CB, then △ABX ≅ △CBX
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | m∠ABX = m∠XBC | if ray BX bisects ∠ABC, then m∠ABX = m∠XBC |
2 | m∠XBC = m∠CBX | m∠XBC = m∠CBX |
3 | m∠ABX = m∠CBX | if m∠ABX = m∠XBC and m∠XBC = m∠CBX, then m∠ABX = m∠CBX |
4 | distance BX = distance BX | distance BX = distance BX |
5 | △ABX ≅ △CBX | if distance AB = distance CB and m∠ABX = m∠CBX and distance BX = distance BX, then △ABX ≅ △CBX |
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