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

- max1409

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- max1409

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

- max1409

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

- max1409

@MasonP

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## More answers

- max1409

@pooja195

- max1409

@FlamePlaysMC

- anonymous

oh im not sure but @paki might be able to help when he gets on

- max1409

@paki please help

- max1409

anyone

- max1409

@pooja195 please help

- anonymous

people probably still sleep or sum

- anonymous

pooja just got online

- max1409

anyone?

- max1409

@pooja please help

- max1409

@pooja195

- max1409

@destinystaggs

- max1409

i am so confused

- max1409

do you get it

- pooja195

I suck at geometry ;-;

- max1409

@pooja195 do yo know anyone who can help me

- max1409

?

- anonymous

well we know that these are angles and lines and there asking which is a right statement

- max1409

they are asking for errors

- anonymous

|dw:1438177982190:dw|

- max1409

i am still confused

- anonymous

this one is right so this one is not it

- max1409

so how do i find the error

- anonymous

idk im still trying to figure this out im sorry

- max1409

?

- random231

you have to check step by step

- max1409

k can you help me

- max1409

@Smita12:

- random231

yeah do u know what CPCT is?

- max1409

no

- max1409

CPCTC is an acronym for corresponding parts of congruent triangles are congruent. CPCTC is commonly used at or near the end of a proof which asks the student to show that two angles or two sides are congruent.

- random231

its a property (Corresponding Pairs Of Congruent Triangles)

- random231

yeah...

- max1409

so what should i do

- random231

so you must have noticed in step 6 it is mentioned:: OL ≅ ON CPCTC

- max1409

no ol is not on cptc

- max1409

so

- max1409

so should i write OL ≅ ON in not cpctc

- random231

how can that be true before it is proved that the triangles are congruent which has been proved in step8

- random231

no its the property of isosceles triangle ie ∠OLN ≅ ∠LNO Given

- max1409

so what should i write ?

- max1409

i am really bad at geometry

- max1409

?

- random231

you should write OL ≅ ON (opposite sides of an isosceles triangle)

- max1409

whats the second error ?

- random231

im trying to identify it. :P

- max1409

k

- max1409

did you find the second error

- random231

im trying bro

- max1409

k

- max1409

this is so hard

- random231

its not so hard and i dont think there is another error at all. every step seems perfect

- max1409

did you find it?

- random231

nahh im sorry!!

- max1409

darn

- max1409

i am so stuck lol i have been trying to figure this out for 1 hour

- max1409

@satellite73

- max1409

?

- random231

@satellite73 can you please help him?

- max1409

@nogoodatgeometry @alexistheking777

- anonymous

is there a picture for this proof?

- max1409

no picture

- max1409

just the two column proof

- anonymous

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

- max1409

?

- anonymous

do you have an idea of what the incorrect ones are?

- max1409

step 6 is incorrect

- max1409

but i can't find the second one

- max1409

?

- anonymous

hang on a second

- max1409

k

- anonymous

|dw:1438180391633:dw|

- anonymous

here are your triangles

- max1409

k

- anonymous

now why is step 6 incorrect?

- max1409

because OL ≅ ON is opposite sides of an isosceles triangle.

- max1409

?

- anonymous

but they are still congruent

- max1409

ohh ok

- max1409

i am really confused now

- anonymous

what does CPCTE mean?

- max1409

corresponding parts congruent triangles

- anonymous

yes. but the statement dosent say that they are equal, it says their congruent. you were right about 6 being wrong. but i wanted for you to know why

- max1409

k

- anonymous

for the statement to be true it should either be
OL ≅ ON Reflexive property
or
OL = ON CPCTE

- max1409

k

- anonymous

so whats the second one and why?

- max1409

i am not sure

- max1409

can you help me find the second one

- anonymous

yeah. look at all of the signs and wording

- max1409

is the second error 5 LE ≅ EN Definition of a Perpendicular Bisector

- anonymous

nope

- anonymous

look at number 8. do you see anything wrong?

- max1409

it does not look like an asa triangle

- anonymous

what congruence postulate would fit here?

- anonymous

how about SSS?

- max1409

k

- max1409

so how should i write my answer?

- anonymous

no i was asking if SSS looked right

- anonymous

does it?

- max1409

yes

- max1409

?

- max1409

?

- anonymous

8 OLE ≅ ΔONE SIde-Side-Side (SSS) Postulate

- max1409

k so should i write statement 6 and 8 are wrong.

- max1409

or do i have to explain?

- anonymous

correct the error

- max1409

can you help me write out the answer?

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