Question

Please help me:

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. Identify and correct the errors.

Answer 1

Meaning they're able to help me? Lol

Answer 2

@Vocaloid

Answer 3

Typically in such questions, it is best to either prove it yourself before looking at their proof or follow along with their proof until you notice an error.

Everything seems great until step 4 - your proved that m∠LEO = 90° and m∠NEO=90°, but there is no such statement that m∠LEO=m∠NEO directly after to move straight to the congruence theorem in step 6. You need to prove they are equivalent, and that can be done using the transitive property. Since m∠LEO=90 and m∠NEO=90, m∠NEO=m∠LEO. You could shift step 7 after step 4.


Step 6 has the error of by using the HL postulate. When you follow along, you find out that you have two triangles formed from a perpendicular bisector, where there is an angle, then a side, then an angle. Although we may be tempted to use the HL postulate, it is not possible as there is no proof that the hypotenuse and one leg are congruent. Instead, what do you think the triangle congruence theorem should be?