Question

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Answer 1

Answer:

Coordinates of Point A and C are (6,8) and (8,4).

Coordinates of Point D and E are ,(4,5) and (5,3).

→Length of segment DE

  Using Distance Formula

$=\sqrt{(5-4)^2+(5-3)^2}\\\\=\sqrt{1+4}\\\\=\sqrt{5}$

$AC=\sqrt{(8-6)^2+(8-4)^2}\\\\=\sqrt{4+16}\\\\=\sqrt{20}\\\\=2\sqrt{5}$

→So,Length of segment AC=2√5

→By substitution

$DE=\frac{AC}{2}$

→By the slope formula, which is

    $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\ \text{Slope of Segment DE}=\frac{5-3}{4-5}\\\\=-2\\\\\text{Slope of Segment AC}=\frac{8-4}{6-8}\\\\=\frac{4}{-2}\\\\=-2$

→When Slopes are equal, lines are Parallel.

So, Segment DE ║ Segment AC

The following Statement completes the proof,which is Missing

 Option D: By the slope formula

Answer 2

Answer:

Step-by-step explanation:

Statement Reason:

1) The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula

2) Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5 By the distance formula

3) Segment DE is half the length of segment AC By substitution

4) Slope of segment DE is -2 and slope of segment AC is -2 by the slope formula

5) Segment DE is parallel to segment AC Slopes of parallel lines are equal...