Question

A classmate says that line AB is parallel to line DC based on the diagram belowe. Explain the error.

Answer 1

attachment of diagram

Answer 2

tha diagram is wrong

Answer 3

oh thanks i didnt realize.... :P *sarcasm*

Answer 4

could you elaborate ?

Answer 5

lol well there's no ducks in it

Answer 6

ohhhhh yesssss, very wise.. im sure my teacher will approve

Answer 7

make a drawing of a duck it should help allot better with your math problem :D

Answer 8

i cant draw duckies :P I can draw a house tho ! CAD 2 like waddup

Answer 9

XD

Answer 10

lol ughhhh somebody who is qualified plz explain what is wrong with this diagrammmmmm

Answer 11

wat do you think, they're parallel ?

Answer 12

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Answer 13

im supposed to explain that they arent parallel

Answer 14

yup, before u explain, you need to convince urself that they're not parallel right ?

Answer 15

to be exact - you need to convince urself that, we cannot say they're parallel

Answer 16

it looks pretty durn parallel to me. i dont know how to say it isnt

Answer 17

Meniether...

Answer 18

Is this a multiple choice question? If so, what are the answers?

Answer 19

its an essay :P

Answer 20

even if it looks parallel, it doesn't necessarily mean that it is indeed parallel. Now you just need to prove it with the given information

Answer 21

you dont know how Z, X hit

they can be anything and the opposite 90°
have no real relation to each other

Answer 22

The actual error was in applying the \(\large \text{alternate interior angles theorem} \) incorrectly. The student arrived at the conclusion that AB || CD because, he thought WZ adn XY are parallel, but they're not given as parallel. He **assumed** them to be parallel, which is a serious offense in geometry proofs.

Answer 23

How does the relation between WZ and XY determine the relation between AB and DC ??

Answer 24

Once he made that error, \(\angle WZY \cong \angle XYC\) by corresponding angles postulate. then by applying \(\large \text{alternate interior angles theorem }\) , he concluded that AB || CD

Answer 25

ohhhhhhhhhhh I can seeeee ! :O

Answer 26

grazie grazie grazie !

Answer 27

basically the angles are only the same when the line it goes through is parallel

Answer 28

also observe that, we're given \(\angle AWZ \cong \angle XYC \).
so its very easy to get fooled !

Answer 29

and if WZ , XY are parallel they are 2 lines with exact same angles there

Answer 30

so if WZ ,XY are parallel you can basically put one onto the other
and treat them added like one line with two angle information
and two angle information is enough to determine parallelity

Answer 31

you can "overlay" WZ, XY if they're really parallel and get one piece of info from each one ;)