Proof: Bisector SAS 2

Let's prove the following theorem:

if ray BX bisects ∠ABC and distance AB = distance CB, then △ABX ≅ △CBX

A C X B

Proof:

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Given
1 ray BX bisects ∠ABC
2 distance AB = distance CB
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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