Question

Theorem: The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. A two column proof of the theorem is shown, but a justification is missing.

A triangle with vertices A at 6, 8. B is at 2, 2. C is at 8, 4. Segment DE. Point D is on side AB and point E is on side BC

Statement Justification
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) Midpoint Formula
Length of segment DE is Square root of 5 and length of segment AC is 2 multiplied by the square root of 5. Distance Formula
Segment DE is half the length of segment AC. Substitution Property of Equality
Slope of segment DE is −2 and slope of segment AC is −2.
Segment DE is parallel to segment AC. Slopes of parallel lines are equal.


Which is the missing justification?

Additive Identity
Midsegment Theorem
Slope Formula
Transitive Property of Equality

Answer 1

Answer:by the slope formula

Explanation:

Answer 2

Answer: The slope formula

Explanation:

To calculate the slope (m) of a line segment with endpoints
`(x_1,y_1)` and {tex}(x_2,_2)[/tex] is given by
`m=(y_2-y_1)/(x_2-x_1)`

So to find the slope of line segment DE with endpoints D=(4,5) and E=(5,3)

`m_1=(3-5)/(5-4)=(-2)/(1)=-2`

The slope of line segment AC with endpoints A=(6,8) and C=(8,4)

`m=(4-8)/(8-6)=(-4)/(2)=-2`

Thus, Slope of segment DE is −2 and slope of segment AC is −2 by slope formula.