Question

Statement Reason The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the 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 By the distance formula Segment DE is half the length of segment AC Slope of segment DE is −2 and slope of segment AC is −2 By the slope formula Segment DE is parallel to segment AC Slopes of parallel lines are equal Which of the following completes the proof?

Answer 1

The most logical order is:
- The coordinates of point D and E by the midpoint formula.
- Slope of segment DE and slope of segment AC.
- Segment DE is parallel to segment AC. Slopes of parallel lines are equal.
- Length of segment DE and length of segment AC by the distance formula.
- Segment DE is half the length of segment AC by the substitution.
Answer: B ) III, V, II, IV, I. Hope this helps 

Answer 2

so what is the asnwer if these are the choices

1 By definition of congruence

2Addition property of equality

3By construction

4By the slope formula

Statement Reason

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

Segment DE is half the length of segment AC By substitution

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 of the following completes the proof?