Question

Sterling has prepared the following two-column proof below. He is given that ∠OLN ≅ ∠LNO and he is trying to prove that OL ≅ ON.

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 ΔOLE ≅ ΔONE Hypotenuse-Leg (HL) Postulate
7 ∠LEO ≅ ∠NEO Transitive Property of Equality
8 OL ≅ ON CPCTC
Sterling made two errors in the proof.

Answer 1

Is there a picture of the triangle?

Answer 2

Okay, straight away, I can tell you that 8 and 7 should be switched. CPCTC should never be the last proof.

Answer 3

Ok that makes sense

Answer 4

@Seratul what would be the second one?

Answer 5

Still looking.

Answer 6

Oh, I don't think that is the correct property.

Answer 7

Wait, i'm sorry. 7 and 8 shouldn't be switched, there should be a 9. 7 is correct. I think you should get another opinion on this by someone else. I'm can't really remember that well. Maybe @triciaal can help. She's really good at math.

Answer 8

ok thanks anyway.

Answer 9

thanks but I prefer Algebra so I don't have to think

Answer 10

let me look give me a min

Answer 11

ok thanks @triciaal

Answer 12

@mathstudent55 ?

Answer 13

@pooja195 please check thanks

Answer 14

If anyone can help that would be great.

Answer 15

\[\Huge\color{orange}\checkmark \]

Answer 16

All that was given are those two equal angles...
I don't think you can assume a perpendicular bisector OE, just a perpendicular OE, so you cant say LE=NE...but
I think you have to assume this is ok to do that since there are more errors in the proof

Answer 17

1) Angles OLN = ONL -----given
2) Draw perpendicular altitude OE ----- Construction
3) angle LEO = 90 -----def of perpendicular altitude
4) angle NEO = 90 -----def of perpendicular altitude
5) angles LEO=NEO ----- transitive
6) OE = OE ----- reflexive
7) Triangles OEL = OEN are congruent ----- angle-angle-side
8) ON=OL -----CPCTC

Answer 18

that is what i would put