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.

Answer 1

https://lee.flvs.net/webdav/assessment_images/educator_geometry_v16/03_02b_05_01.gif

Answer 2

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
I am thinking Angle Side Angle is wrong but I am not sure

Answer 3

I cannot see the image, it requires an account, could you take a screenshot and upload it here?

Answer 4

sure hold on a sec

Answer 5

It is literally the last question on my test and I am stumped

Answer 6

I believe you are correct

Answer 7

I thought so to however I forgot to post something. Gideon made two errors in the proof. Identify and correct the errors.

Answer 8

I think 5 is wrong not sure though

Answer 9

Do you know of anybody who could solve it? If so let them know please.

Answer 10

not anyone on but if they come on @dude @563blackghost

Answer 11

two great mafers right der^

Answer 12

Thanks

I will message them.

Answer 13

I will give a medal to whoever answers this. I and desperate as my test was due last
week

Answer 14

I know six is wrong because CPCTC is Corresponding Parts of Congruent Triangles are Congruent. I don't think that works here.

Answer 15

Thanks for the help. I submitted the test and I am waiting for the results

Answer 16

Where is point E?

Answer 17

point is in the middle of line NL you cant see it in the picture but point E is made by construction

Answer 18

it is what allows for the line bisector

Answer 19

Mmm the visual would help ;-;

Answer 20

I don't need the help anymore as I tried to figure it out and I submitted it. However I can send you the pic to see what you think the answer is?

Answer 21

Ye I know, but I thought maybeh you would still like an explanation for it >.<

pls do send a pic

Answer 22

Alright I will give me a sec

Answer 23

Here it is

Answer 24

I would agree with your answer, the final proven triangle is named as \(\bf{\angle OLE}\) by ASA, but we did not prove it in that way. He never determined that \(\angle O = \angle O\) instead it is proven by SAS Theorem. Considering that LO = NO by CPTCTC, and given that \(\angle L\) = \(\angle N\) with two equal lengths from the bisector. So side-angle-side.

Answer 25

CPCTC does apply. You proved an angle, then a side, and then another angle, so you had proved a triangle already, meaning the other not mentioned sides are equal.

Answer 26

Isn't it the Transitive Property of Equality? What I said in my answer was what you mentioned about the Side Angle Side and that the Substitution property of equality should have been the Transitive.