Mathematics, 24.01.2020 23:31 IsabellaGracie

Theorem: a line parallel to one side of a triangle divides the other two proportionately. in the figure below, segment de is parallel to segment bc and segment ef is parallel to ab:
which statement can be proved true using the given theorem?

a. segment bd = 12
b. segment bd= 4
c. segment bf= 16
d. segment bf= 9

Theorem: a line parallel to one side of a triangle divides the other two proportionately. in the fi

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Answer from: nanaflower321

C. Segment BF= 16

Step-by-step explanation:

Since the line EF cuts AD and BD proportionally, we can deduce the following:

$\frac{AE}{EC} = \frac{BF}{FD}$

We can then isolate BF, that way:

$BF = \frac{AE * FD}{EC} = \frac{12 * 24}{18} = \frac{288}{18} = 16$

So, segment BF = 16.

We can also find segment BD the same way:

$BD = \frac{AD * EC}{AE} = \frac{6 * 18}{12} = \frac{108}{12} = 9$

But BD = 9 isn't in the possible answers.

Answer from: jay8682

The correct option is

Step-by-step explanation: We are given the following theorem :

"A line parallel to one side of a triangle divides the other two proportionately".

In the figure, segment DE is parallel to segment BC and segment EF is parallel to AB.

We are to select the statement that can be proved using the above theorem.

From the figure, we note that in triangle ABC,

AD = 6, AE = 12, CE = 18 and CF = 24.

Since DE is parallel to BC, so we get

$\dfrac{AD}{BD}=\dfrac{AE}{CE}\\\\\\\Rightarrow \dfrac{6}{BD}=\dfrac{12}{18}\\\\\\\Rightarrow \dfrac{6}{BD}=\dfrac{2}{3}\\\\\\\Rightarrow BD=\dfrac{18}{2}\\\\\Rightarrow BD=9.$

Also, since EF is parallel to AB, so we get

$\dfrac{CE}{AE}=\dfrac{CF}{BF}\\\\\\\Rightarrow \dfrac{18}{12}=\dfrac{24}{BF}\\\\\\\Rightarrow \dfrac{3}{2}=\dfrac{24}{BF}\\\\\\\Rightarrow BF=\dfrac{48}{3}\\\\\Rightarrow BF=16.$

Thus, the required true statement is BF = 16.

Option (C) is CORRECT.

Answer from: Quest

The probability of picking 2 green markers is 2/10

Answer from: Quest

starting with:

5 + x - 12 = 2x - 7

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)

5 - 12 = x - 7 (combine and cancel x's from both sides)

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)

0 = x (add numbers together on both sides)

so in order for the equation to be true, x must be 0.

trying x = -0.5

5 + x - 12 = 2x - 7 (original equation)

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)

5 + -0.5 - 12 = -1 - 7 (did multiplication)

-7.5 = -8 (did addition on both sides)

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.

trying x = 0

5 + x - 12 = 2x - 7 (original equation)

5 + 0 - 12 = 2(0) - 7 (plug in value of x)

5 + 0 - 12 = 0 - 7 (did multiplication)

-7 = -7 (did addition on both sides)

since -7 equals -7, that demonstrates that the value of 0 for x is correct.

trying x = 1

5 + x - 12 = 2x - 7 (original equation)

5 + 1 - 12 = 2(1) - 7 (plug in value of x)

5 + 1 - 12 = 2 - 7 (did multiplication)

-6 = -5 (did addition on both sides)

since -6 is obviously not equal to -5, the value of 1 for x is wrong.

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