Earl and Sean provide the following proofs for vertical angles to be equal.

Question

anonymous · Answer

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anonymous · Answer

Earl’s proof:   angle 1 + angle 2 = 180° (PQ is a straight line)
                      angle 3 + angle 4 = 180°(PQ is a straight line)
                      Therefore, angle 1 + angle 2 = angle 3 + angle 4
                      Hence, vertical angles are equal.  

Sean’s proof:  angle 1 + angle 4 = 180° (transversal t is a straight line)
                      angle 2 + angle 3 = 180°(transversal t is a straight line)
                      Therefore, angle 1 + angle 4 = angle 2 + angle 3
                      Hence, vertical angles are equal.  
 
Which statement is correct?

anonymous · Answer

Answer choices: Only Earl’s proof is correct.
		
Only Sean’s proof is correct.
		
Both Earl’s and Sean’s proofs are correct.
		
Both Earl’s and Sean’s proofs are incorrect.

anonymous · Answer

Both Earl’s and Sean’s proofs are correct.

anonymous · Answer

I'll go ahead and disagree with Lilysue.

anonymous · Answer

Why?

anonymous · Answer

It's not that they haven't said anything incorrect. They just haven't said enough to prove the statement.

anonymous · Answer

A + B = 10
C + D = 10
Can I say that A = C? Or A=D? Or anything at all?

anonymous · Answer

Thanks guys

anonymous · Answer

-_-
Haha okay, guys.

anonymous · Answer

These guys are wrong. Not tryin' to be a jerk about it, but they are.

anonymous · Answer

Sorry SmoothMath but I'm gonna go with my bro on this one

anonymous · Answer

Does your bro have a degree in mathematics?

anonymous · Answer

Has he ever taken a proofs course?

anonymous · Answer

I dunno

anonymous · Answer

He hasn't. Or else he failed it.

anonymous · Answer

Well what do you think is the right answer?

anonymous · Answer

Since your so smart

anonymous · Answer

Evergirl, Earl's arguement goes like this:
1+2 = 180
3+4 = 180
Therefore, 1 = 3 and 2=4
Can you conclude the third thing from those first two things?

Let me make a similar argument which turns out to be invalid
A = 2 B = 8 C=4 D=6
A + B = 10
C + D = 10
Therefore, A = C and B = D

anonymous · Answer

Ok Thanks guys ;)

anonymous · Answer

No, I get that. That's cool. It's just that... you're wrong. Lols. And it's frustrating as a professional to be ignored in favor of someone with very little expertise.

anonymous · Answer

Here's the correct proof:

1 +4 =180 because they form a straight line.
3 +4 = 180 because they form a straight line.
1+4 = 3 + 4, therefore 1=3 and vertical angles are congruent.