In triangle abc shown below, side ab is 8 and side ac is 6: triangle abc with segment joining point d on segment ab and point e on segment ac. which statement is needed to prove that segment de is half the length of segment bc? segment ad is 3, and segment ae is 4. segment ad is 3, and segment ae is 6. segment ad is 4, and segment ae is 6. segment ad is 4, and segment ae is 3.

Segment AD is 4, and segment AE is 3.

Step-by-step explanation:

Given,

In triangle ABC,

AB = 8 unit,

AC = 6 unit,

We have to prove :

[tex]DE=\frac{BC}{2}{/tex]

By the Midpoint Theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Thus, for proving the required statement we need to prove D and E are midpoints of AB and AC respectively,

That is, AD = DB and AE = EC

∵ AB = 8 ⇒ AD + DB = 8 ⇒ AD + AD = 8 ⇒ 2AD = 8 ⇒ AD = 4

Similarly,

2AE = 6 ⇒ AE = 3

Hence, LAST option is correct.

so, converting firstly the mixed fractions to improper fractions and then "adding".

addition

step-by-step explanation: