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In the diagram below, \(\overline{AD}\parallel\overline{BE}\) and  \(A\) is not on \(\overline{BC}.\)

https://latex.artofproblemsolving.com/6/d/9/6d98aacdad1bdb92383a3fb9b284a630fa987ab0.png <----- Here's the image. Sorry if it's super dark and hard to read.

 

Can \(\angle CAD=\angle CBE?\) Explain.

 Dec 12, 2019
 #1
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Angle E  and angle D  are equal

For CBE and CAD to be equal the remaining angle of the triangles would als have to be equal (because all angles of a triangle add to 180)

 

angle ACD is not equal to BCD    so   CAD cannot equal CBE

 Dec 12, 2019
 #2
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Angles CAD and CBE can be equal!  We can't let A be on BC, but we can adjust the position of B so that AC and BC are very close to each other.  Then if they are close enough, since AD and BE are parallel, we can say make

 Dec 12, 2019
 #3
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That's right, angle CAD can be equal to angle CBE.  If angles CAD and CBE are not equal, then we can choose a point A' on AD so that angle CA'D is equal to CBE.  So we can move point A to A', and then angles CAD and CBE will be equal.

 Dec 12, 2019
 #6
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Then A' would be on BC which the question states is not allowed.

ElectricPavlov  Dec 12, 2019
 #4
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But if you measure the diagram, then angle CAD is about 44 degrees, and angle CBE is 46 degrees.  How can they be equal?

 Dec 12, 2019
 #5
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Because the diagram is not necessarily to scale...

Guest Dec 12, 2019
 #7
avatar+108626 
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I think thisis the pic?

 

 Dec 12, 2019
 #8
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yes it is 

Guest Dec 13, 2019

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