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3 years ago

In triangle ABC shown below, side AB is 8 and side AC is 6:

Mathematics

2 answers:

lbvjy [14]3 years ago

8 0

Segment AD is 4, and segment AE is 3. This is because AB is 8, and half of 8 is 4, and then AC is 6, and half of 6 is 3.

Gekata [30.6K]3 years ago

4 0

Answer:

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.

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Which statement best explains the relationship between lines FG and HJ?

murzikaleks [220]

Answer:

(D)

Step-by-step explanation:

From the figure, we have

The coordinates of the point F are: (-4,1).

The coordinates of the point G are: (0,-2)

The coordinates of the point J are: (0,4) and

The coordinates of the point H are: (-4,-2).

Now, the slope of the line FG is :

$S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$S=\frac{-2-1}{0+4}$

$S=\frac{-3}{4}$

And, the slope of the line HJ is:

$S=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$S=\frac{-2-4}{-4-0}$

$S=\frac{3}{2}$

Now, $the slope of FG=\frac{1}{slope of HJ}$

$\frac{-3}{4}=\frac{2}{3}$

which is not possible, thus They are not perpendicular because their slopes are not negative reciprocals.

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Answer:

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