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.

Guest Dec 12, 2019

#1**0 **

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

ElectricPavlov 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

Guest 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.

Guest Dec 12, 2019