Question

The flow chart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side.
Which statement and reason can be used to fill in the numbered blank spaces?

Answer 1

Given: In ∆ABC below,BD over BA equals BE over BC .
Prove: segment DE is parallel to segment AC

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1002_03/image0024e983525.gif

Answer 2

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1002_03/1002_03_01_a.jpg

Answer 3

Answers:
1. ∡BDE ≅ ∡BAC
2. Corresponding Parts of Similar Triangles

1. ∡BDE ≅ ∡BCA
2. Alternate Exterior Theorem

1. ∡BDE ≅ ∡BAC
2. Corresponding Angles Postulate

1. ∡BDE ≅ ∡BCA
2. Corresponding Parts of Similar Triangles

I think its alternate exterior

Answer 4

since we are proving similarity by SAS so we must find a similar angle between the two triangle
and since B is same for both it can be used in the proof

so the answer is
1 ∡B ≅ ∡B
2 Reflexive Property of Equality

Answer 5

That's not one of the answers though?

Answer 6

it's the last option. ..
1. ∡BDE ≅ ∡BCA
2. Corresponding Parts of Similar Triangles

Answer 7

Nope its not, already tried that one

Answer 8

please help!

Answer 9

Its not alternate angles either.

Answer 10

converse of corresponding-angles postulate is :
if corresponding angles are congruent, then the two lines are parallel

Answer 11

look at the triangle pix, since they are similar, corresponding angles of similar triangles are congruent :
∡BDE ≅ ∡BAC