Proof: Vertical Angles ASA

Let's prove the following theorem:

if M is the midpoint of line AB and m∠XMY = 180 and ∠MAY is a right angle and ∠MBX is a right angle, then △YMA ≅ △XMB

A Y B X M

Proof:

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Given
1 M is the midpoint of line AB
2 m∠XMY = 180
3 ∠MAY is a right angle
4 ∠MBX is a right angle
Proof Table
# Claim Reason
1 distance AM = distance MB if M is the midpoint of line AB, then distance AM = distance MB
2 distance MA = distance AM distance MA = distance AM
3 distance MA = distance MB if distance MA = distance AM and distance AM = distance MB, then distance MA = distance MB
4 m∠AMB = 180 if M is the midpoint of line AB, then m∠AMB = 180
5 m∠YMA = m∠XMB if m∠XMY = 180 and m∠AMB = 180, then m∠YMA = m∠XMB
6 m∠MAY = 90 if ∠MAY is a right angle, then m∠MAY = 90
7 m∠MBX = 90 if ∠MBX is a right angle, then m∠MBX = 90
8 m∠MAY = m∠MBX if m∠MAY = 90 and m∠MBX = 90, then m∠MAY = m∠MBX
9 △YMA ≅ △XMB if m∠YMA = m∠XMB and distance MA = distance MB and m∠MAY = m∠MBX, then △YMA ≅ △XMB

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