Proof: Bisector Angle
Let's prove the following theorem:
if PX ⊥ XY and PZ ⊥ ZY and distance XP = distance ZP, then m∠PYX = m∠PYZ
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | ∠PZY is a right angle | if PZ ⊥ ZY, then ∠PZY is a right angle |
2 | ∠YZP is a right angle | if ∠PZY is a right angle, then ∠YZP is a right angle |
3 | ∠PXY is a right angle | if PX ⊥ XY, then ∠PXY is a right angle |
4 | ∠YXP is a right angle | if ∠PXY is a right angle, then ∠YXP is a right angle |
5 | distance YP = distance YP | distance YP = distance YP |
6 | △YXP ≅ △YZP | if ∠YXP is a right angle and ∠YZP is a right angle and distance YP = distance YP and distance XP = distance ZP, then △YXP ≅ △YZP |
7 | m∠PYX = m∠PYZ | if △YXP ≅ △YZP, then m∠PYX = m∠PYZ |
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