Nina has prepared the following two-column proof below. She is given that ?OLN ?

Question

Nina has prepared the following two-column proof below. She is given that ?OLN ? ?LNO and she is trying to prove that OL ? ON.

Nina made two errors in the proof. Identify and correct the errors.

Step Statement Reason 1 ?OLN ? ?LNO Given 2 Draw OE as a perpendicular bisector to LN by Construction 3 ?LEO ? ?NEO Transitive Property of Equality 4 m?LEO = 90° Definition of a Perpendicular Bisector 5 m?NEO = 90° Definition of a Perpendicular Bisector 6 LE ? EN Definition of a Perpendicular Bisector 7 ?OLE ? ?ONE Side-Angle-Side (SAS) Postulate 8 OL ? ON CPCTC

Explanation / Answer

step 2 : let OE is just perpendicular to LN, because we cannot confirm that perpendicular bisector of LN passes through O.

now step 6 is removed

step 7 : OLE ONE by Angle-Angle (AA) postulate ( OLN LNO and LEO NEO = 90° )

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