Question

Gideon has prepared the following two-column proof below. He is given that ∠OLN ≅ ∠LNO and he is trying to prove that ΔOLE ≅ ΔONE.

Triangle OLN, where angle OLN is congruent to angle LNO

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

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

I kinda feel like step 6 and 7 are wrong i just need to know what to replace them with especially step 6 ........ please don't use answers from another post about this question

Answer 1

i think will be more usefuly than you drawing these - you will can understanding more easy and clearly

Answer 2

@ThisGirlPretty

Answer 3

@ThisGirlPretty any idea please ?

Answer 4

do you agree that step 6 and 7 are wrong ?

Answer 5

but in the steps 3 and 4 wrote that angle LEO and angle NEO has 90 degree

do you agree this ?

Answer 6

are these right angles sure ?

Answer 7

no not are so from this result what ? => that step 3 and 4 are wrong - yes ?

Answer 8

@jhonyy9 NO, I went over these with some of my friends and all of them are saying step 6 and 7. I already know how to correct step 7 Its just step 6 I'm having trouble with.. I'm debating whether or not to move it as the final step