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padilas [110]
3 years ago
7

Which method do you prefer to use: Trig Method or Special Right Triangles

Mathematics
1 answer:
kondaur [170]3 years ago
8 0

Answer:

would use the Trig Method.

Step-by-step explanation:

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Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC
Vinvika [58]

According to the midsegment theorem, the midsegments are parallel to

and half the length of the opposite side.

The completed statement are as follows;

  • Because the slopes of \overline{EF} and \overline{AC} are both<u> -4</u>, \overline{EF} ║ \overline{AC}
  • EF = \underline{\sqrt{17}} and AC = \underline{2 \cdot \sqrt{17} }
  • Because \underline{\sqrt{17} } = \underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }, EF = \frac{1}{2} \cdot AC

<u />

Reasons:

From the given graph of ΔABC, we have;

Coordinates of the points <em>A</em>, <em>B</em>, and <em>C </em>are; A(-5, 2), B(1, -2), and C(-3, -6)

The coordinates of the point D and E on \mathbf{\overline{DE}} are; D(-4, -2), and E(-2, 0)

The coordinates of the point F is; F(-1, -4)

  • Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}

\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)}  = \frac{-8}{2}} = -4

\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)}  = \frac{4}{-1} = -4

  • Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1}  \right )^{2}+\left (y_{2}-y_{1}  \right )^{2}}

Length of EF  = √((-1 - (-2))² + (-4 - 0)²) = √(17)

Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)

Therefore, we have;

Because the slope of \mathbf{\overline {EF}} and \mathbf{\overline {AC}} are both , <u>-4</u>, \overline {EF} ║ \overline {AC}. EF = \underline{\sqrt{17}}, and AC

= \underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}},. Because \underline{\sqrt{17}} = \underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}, EF =\mathbf{ \frac{1}{2} AC}

Learn more about midsegment theorem of a triangle here:

brainly.com/question/7423948

8 0
3 years ago
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