Proof: Exterior Angle is Greater

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	distance XM = distance MP	if M is the midpoint of line XP, then distance XM = distance MP (Midpoint Property)
2	distance XM = distance PM	if distance XM = distance MP, then distance XM = distance PM (Distance Property 2)
3	distance YM = distance MZ	if M is the midpoint of line YZ, then distance YM = distance MZ (Midpoint Property)
4	distance MY = distance MZ	if distance YM = distance MZ, then distance MY = distance MZ (Distance Property 1)
5	m∠YMZ = 180	if M is the midpoint of line YZ, then m∠YMZ = 180 (Angle Formed by Midpoint)
6	m∠ZMY = 180	if m∠YMZ = 180, then m∠ZMY = 180 (Angle Symmetry Example 2)
7	m∠XMP = 180	if M is the midpoint of line XP, then m∠XMP = 180 (Angle Formed by Midpoint)
8	m∠PMX = 180	if m∠XMP = 180, then m∠PMX = 180 (Angle Symmetry Example 2)
9	m∠XMY = m∠PMZ	if m∠PMX = 180 and m∠ZMY = 180, then m∠XMY = m∠PMZ (Vertical Angles)
10	△XMY ≅ △PMZ	if distance XM = distance PM and m∠XMY = m∠PMZ and distance MY = distance MZ, then △XMY ≅ △PMZ (SAS Property)
11	m∠MYX = m∠MZP	if △XMY ≅ △PMZ, then m∠MYX = m∠MZP (Congruent Triangles Property 6)
12	m∠MZP = m∠MYX	if m∠MYX = m∠MZP, then m∠MZP = m∠MYX (Symmetric Property of Equality)
13	point M is in segment YZ	if M is the midpoint of line YZ, then point M is in segment YZ (Midpoint is in Segment)
14	point P lies in interior of ∠YZE	if point M is in segment YZ and m∠XMP = 180 and m∠XZE = 180, then point P lies in interior of ∠YZE (Interior of an Angle)
15	m∠YZE = (m∠YZP) + (m∠PZE)	if point P lies in interior of ∠YZE, then m∠YZE = (m∠YZP) + (m∠PZE) (Angle Addition Theorem)
16	m∠YZE > m∠YZP	if m∠YZE = (m∠YZP) + (m∠PZE) and m∠PZE > 0, then m∠YZE > m∠YZP (Greater Than Property)
17	m∠YZP = m∠MZP	if m∠ZMY = 180, then m∠YZP = m∠MZP (Collinear Angles B)
18	m∠YZP = m∠MYX	if m∠YZP = m∠MZP and m∠MZP = m∠MYX, then m∠YZP = m∠MYX (Transitive Property of Equality)
19	m∠MYX = m∠ZYX	if m∠ZMY = 180, then m∠MYX = m∠ZYX (Collinear Points Property)
20	m∠YZP = m∠ZYX	if m∠YZP = m∠MYX and m∠MYX = m∠ZYX, then m∠YZP = m∠ZYX (Transitive Property of Equality)
21	m∠YZE > m∠ZYX	if m∠YZE > m∠YZP and m∠YZP = m∠ZYX, then m∠YZE > m∠ZYX (Transitive Property of Inequality 3)
22	m∠ZYX < m∠YZE	if m∠YZE > m∠ZYX, then m∠ZYX < m∠YZE (Symmetric Inequality Property)

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