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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
+21725
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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
+1

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
+1

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
+21725
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Then A' would be on BC which the question states is not allowed.

ElectricPavlov  Dec 12, 2019
#4
+1

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
+1

Because the diagram is not necessarily to scale...

Guest Dec 12, 2019
#7
+108626
+1

I think thisis the pic?

Dec 12, 2019
#8
0

yes it is

Guest Dec 13, 2019