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In the diagram below line segment AD is parallel to line segment BE and A is not on line segment BC. Line segments AD and BC intersect at P. Can angle CAD equal angle CBE?

Thank you for your help in advance!

 May 18, 2020
 #1
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Note that if  AD  is parallel to  BE, then corresponding  angles  ADC  and BEC  are equal

 

Thus, in triangles CAD  and CBE, angle ADC  =  angle BEC

 

But  angle ACD >  angle BCE

 

So

 

Then  

 

ADC + ACD  >   BEC + BCE

 

And  because all three  angles in each triangle will sum to 180

 

Then angle CAD  must be less than angle CBE

 

 

cool cool cool

 May 18, 2020

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