Transitive Property of Equality Variation 2
Distance Property 1
Distance Property 2
Distance Property 3
Angle Symmetry Example 2
Collinear Angles Property 9
Transitive Property Application 2
Angles of an Isosceles Triangle
Angle Symmetry Example
Angle Symmetry 2
Isosceles Triangle 2
Transitive Property of Equality Variation 1
Perpendicular to Angle
Collinear Then 180
Subtract Both Sides
Add Term to Both Sides 6
Subtract Both Sides 2
Add Term to Both Sides 7
Vertical Angles
Angle Addition Theorem
Collinear Angles B
Exterior Angle
Exterior Angle B
Collinear Angles Property 10
Collinear Angles Property 3
Collinear Angles Property 3 B
Collinear Angles Property 3 C
alternate interior angles then parallel
ParallelThenAIA
Parallelthenaiashort
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Angle Symmetry B
Substitution Example 10
Substitute First Term
Triangles Sum to 180
Equality Example
If Two Angles Equal Then Three Angles Equal
Angle Angle Side Triangle
Altitudes Isosceles

Proof: Exterior Angle is Greater

Let's prove the following theorem:

if m∠XZE = 180, then m∠ZYX < m∠YZE

Z E X Y M P

Proof:

View as a tree | View dependent proofs | Try proving it

Given
1 m∠XZE = 180
Assumptions
2 M is the midpoint of line YZ
3 M is the midpoint of line XP
4 m∠PZE > 0
Proof Table
# Claim Reason
1 distance XM = distance MP if M is the midpoint of line XP, then distance XM = distance MP
2 distance XM = distance PM if distance XM = distance MP, then distance XM = distance PM
3 distance YM = distance MZ if M is the midpoint of line YZ, then distance YM = distance MZ
4 distance MY = distance MZ if distance YM = distance MZ, then distance MY = distance MZ
5 m∠YMZ = 180 if M is the midpoint of line YZ, then m∠YMZ = 180
6 m∠ZMY = 180 if m∠YMZ = 180, then m∠ZMY = 180
7 m∠XMP = 180 if M is the midpoint of line XP, then m∠XMP = 180
8 m∠PMX = 180 if m∠XMP = 180, then m∠PMX = 180
9 m∠XMY = m∠PMZ if m∠PMX = 180 and m∠ZMY = 180, then m∠XMY = m∠PMZ
10 △XMY ≅ △PMZ if distance XM = distance PM and m∠XMY = m∠PMZ and distance MY = distance MZ, then △XMY ≅ △PMZ
11 m∠MYX = m∠MZP if △XMY ≅ △PMZ, then m∠MYX = m∠MZP
12 m∠MZP = m∠MYX if m∠MYX = m∠MZP, then m∠MZP = m∠MYX
13 point M is in segment YZ if M is the midpoint of line YZ, then point M is in segment YZ
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
15 m∠YZE = (m∠YZP) + (m∠PZE) if point P lies in interior of ∠YZE, then m∠YZE = (m∠YZP) + (m∠PZE)
16 m∠YZE > m∠YZP if m∠YZE = (m∠YZP) + (m∠PZE) and m∠PZE > 0, then m∠YZE > m∠YZP
17 m∠YZP = m∠MZP if m∠ZMY = 180, then m∠YZP = m∠MZP
18 m∠YZP = m∠MYX if m∠YZP = m∠MZP and m∠MZP = m∠MYX, then m∠YZP = m∠MYX
19 m∠MYX = m∠ZYX if m∠ZMY = 180, then m∠MYX = m∠ZYX
20 m∠YZP = m∠ZYX if m∠YZP = m∠MYX and m∠MYX = m∠ZYX, then m∠YZP = m∠ZYX
21 m∠YZE > m∠ZYX if m∠YZE > m∠YZP and m∠YZP = m∠ZYX, then m∠YZE > m∠ZYX
22 m∠ZYX < m∠YZE if m∠YZE > m∠ZYX, then m∠ZYX < m∠YZE
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