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In triangle ABC shown below, side AB is 8 and side AC is 4: 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?

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2goodforschool

I just did the test and got the question right, the answer is:

Segment AD is 4, and segment AE is 2.

Answer with explanation:

Given : In ΔABC,

Length of side AC= 4 cm

Length of side AB= 8 cm

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

Proof:

The theorem of geometry ,which is needed to prove that in ΔABC, BC=2 DE, is →→→→Line Segment Joining the mid point of two sides of triangle is parallel to third side and is half of it.

So, If D and E are mid point of AB and AC,then

→→DE║BC,and, [tex]DE=\frac{BC}{2}[/tex]

So,→ , AD= 4 cm and A E= 2 cm

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