Transitive Property of Equality Variation 2
Collinear Then 180
Converse of the Supplementary Angles Theorem
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Substitution Example 10
Subtract Both Sides
Subtraction Example 2
Add Number to Both Sides
Transitive Property of Equality Variation 1
Angle Symmetry 4
Distance Property 2
If Bisector Then Isosceles
Concurrent

Proof: Concurrent

Let's prove the following theorem:

if A is the midpoint of line XY and B is the midpoint of line ZX and PB ⊥ BX and PA ⊥ AY, then distance PZ = distance PY

P A X Y Z B

Proof:

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Given
1 A is the midpoint of line XY
2 B is the midpoint of line ZX
3 PB ⊥ BX
4 PA ⊥ AY
Proof Table
# Claim Reason
1 distance PX = distance PY if PA ⊥ AY and A is the midpoint of line XY, then distance PX = distance PY
2 distance PZ = distance PX if PB ⊥ BX and B is the midpoint of line ZX, then distance PZ = distance PX
3 distance PZ = distance PY if distance PZ = distance PX and distance PX = distance PY, then distance PZ = distance PY
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