Question

Please help? :)

Answer 1

In Triangle ABC shown below, side AB is 10 and side AC is 8.



Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer
Segment AD is 4 and segment AE is 5.
Segment AD is 5 and segment AE is 4.
Segment AD is 5 and segment AE is 2.
Segment AD is 4 and segment AE is 8.

Answer 2

Segment AD is 5 and segment AE is 4.

Answer 3

Segment AD is 5 and segment AE is 4.
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... because those values would cause AB/AD = AC/AE and along with <A being congruent to itself by the reflexive property, the triangles ADE and ABC are similar by the SAS Similarity Theorem. From the properties of similarity triangles, it can be shown that segment DE is parallel to segment BC and that DE = 1/2 (BC).