Question

Please help me write a 2 column proof AB parallel to DC ; BC parallel to AE prove BC/EA = BD/EB

Answer 1

Answer and Step-by-step explanation:

Since it is given that

AB || DC

BC || AE

Based on this we can conclude that

If AB || DC

So we can say

∠ABE ≅ ∠CDB                  

This indicates that the alternate interior angles are congruent i.e its angle and sides are equal  

Now

If BC || AE  

So we can say  

∠CBD ≅ ∠BEA              

This indicates that the alternate interior angles are congruent i.e its angle and sides are equal  

Now

ΔAEB is same as ΔCBD    

This indicates that in one triangle two angles are same to another two angles so both triangles are similar to each other i.e this is a AA Similarity Postulate  

Finally we proof

$\frac{BC}{EA} = \frac{BD}{EB}$

As the same sides are proportional to each other

We compared both based on interior angles