Complete a triangle proof given that AB is parallel to DE and prove that AB/ED is equal to AC/EC

Question

Two triangles are given, ABC and CDE and they share a common point, C, which connects them forming vertical angles at this point. 

Answer 1

Nisa:

 

Draw the two triangles so the two triangles share point C.  It should look like a bowtie.

 

(1) AB is parallel to DE                   Given

 

(2) Angle A = Angle D                    If two parallel lines are cut by a transversal, alternate interior angles are equal.

     Angle B = Angle E  

 

(3) Angle BCA = Angle DCE            Vertical angles are equal.

 

(4) Triangle BAC is similar to Triangle DEC      If 3 angles in one triangle are equal to three angles in another triangle,                                                                     the triangles are similar.

 

(5) AB/DE = AC/EC                        If two triangles are similar, corresponding sides are proportional.

 

Hope this helps.

 

Denny Rose

Galion, OH