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.
+36915 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
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
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.
+36915 Then A' would be on BC which the question states is not allowed.
