Proof: Bisector Point Equidistant From Sides
Let's prove the following theorem:
if m∠PXY = 90 and m∠PZY = 90 and ray YP bisects ∠XYZ, then distance PX = distance PZ
Proof:
Proof Table
# | Claim | Reason |
---|---|---|
1 | m∠XYP = m∠PYZ | if ray YP bisects ∠XYZ, then m∠XYP = m∠PYZ |
2 | m∠XYP = m∠ZYP | if m∠XYP = m∠PYZ, then m∠XYP = m∠ZYP |
3 | m∠PXY = m∠PZY | if m∠PXY = 90 and m∠PZY = 90, then m∠PXY = m∠PZY |
4 | distance YP = distance YP | distance YP = distance YP |
5 | △XYP ≅ △ZYP | if m∠PXY = m∠PZY and m∠XYP = m∠ZYP and distance YP = distance YP, then △XYP ≅ △ZYP |
6 | distance PX = distance PZ | if △XYP ≅ △ZYP, then distance PX = distance PZ |
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