Question

Please help. the question is in the picture.

Answer 1

We see E is a midpoint so AC:EC=2:1

So our scale factor for similarity must be 2. Let's check the other two sides

AB:ED = 10:5 = 2:1 good

BC:DC = 8:4 = 2:1 good

Each side of ABC is twice its respective side of EDC, so we've shown they're similar.

Answer: Yes

Answer 2

We have measures of all tree sides of the both triangles,

so we can use SSS to check if the triangles are similar.

|ED|/|AB| =5/10=1/2

|DC|/|BC| = 4/8 = 1/2

|EC|/|AC| = 6/12 = 1/2

We see that all tree pairs are in proportion, so these triangles ΔABC and ΔEDC are similar.

We have enough information to prove that ΔABC similar to ΔEDC.