Question

Create a two-column proof of how ▲ABC is similar to ▲ADE (There are no given side lengths or angles)

Answer 1

Dealing with overlapping triangles:


Since BC is marked to be parallel to DE ,
we know that we have <ABC congruent to <BDE (by corresponding angles).
<A is shared by both triangles, so the two triangles are similar by AA.

There is an additional theorem that can be used when working with overlapping triangles:

Additional
Theorem:
If a line is parallel to one side of a triangle and intersects the other two sides of the triangle, the line divides these two sides proportionally.

If BC||DE

Then AB/BD=AC/AE