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Thread: prove a congruent angle with a bisector

  1. #1
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    prove a congruent angle with a bisector

    is this how this is solved?
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  2. #2
    Member Jonboy's Avatar
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    No. Since $\displaystyle \Delta ADP\,\cong \Delta BFP$ then $\displaystyle AP\,=\,PB$.

    A bisector divides a segment into two equal lengths and since they are already equal, then $\displaystyle PE\,=\,KP$

    EDIT: Your title says prove a congruent angle but your file says prove a side is the same. Is that what you intended?


    Last edited by Jonboy; Jun 18th 2007 at 02:12 PM. Reason: confusion
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  3. #3
    Math Engineering Student
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    We can call $\displaystyle \measuredangle~ADK=\alpha\implies\measuredangle~KD P=\measuredangle~EFP=\alpha$, and $\displaystyle \measuredangle~KPD=\measuredangle~EPF\implies$ by ASA congruence we have $\displaystyle \triangle{DKP}\cong\triangle{FEP}\implies\overline {PE}=\overline{KP}\,\blacksquare$
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