Proof: Angles of an Isosceles Triangle

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	distance AM = distance MB	if M is the midpoint of line AB, then distance AM = distance MB (Midpoint Property)
2	distance MA = distance MB	if distance AM = distance MB, then distance MA = distance MB (Distance Property 1)
3	distance XM = distance XM	distance XM = distance XM (Reflexive Property of Equality)
4	△AXM ≅ △BXM	if distance AX = distance BX and distance XM = distance XM and distance MA = distance MB, then △AXM ≅ △BXM (SSS Property)
5	m∠MAX = m∠MBX	if △AXM ≅ △BXM, then m∠MAX = m∠MBX (Congruent Triangles Property 5)
6	m∠AMB = 180	if M is the midpoint of line AB, then m∠AMB = 180 (Angle Formed by Midpoint)
7	m∠MBX = m∠ABX	if m∠AMB = 180, then m∠MBX = m∠ABX (Collinear Points Property)
8	m∠MAX = m∠BAX	if m∠AMB = 180, then m∠MAX = m∠BAX (Collinear Angles Property 9)
9	m∠BAX = m∠ABX	if m∠MAX = m∠MBX and m∠MAX = m∠BAX and m∠MBX = m∠ABX, then m∠BAX = m∠ABX (Transitive Property Application 2)

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