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 the statement and reasons are not in correct order.

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

Statement
Reason
I
Segment DE is half the length of segment AC.
By substitution
II
Segment DE is parallel to segment AC.
Slopes of parallel lines are equal.
III
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3)
By the

Answer 1

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 the statement and reasons are not in correct order.

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

Statement
Reason
I
Segment DE is half the length of segment AC.
By substitution
II
Segment DE is parallel to segment AC.
Slopes of parallel lines are equal.
III
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3)
By the midpoint formula
IV
Length of segment DE is 2 multiplied by the square root of 5.
By the distance formula
V
Slope of segment DE is -2 and slope of segment AC is -2.
By the slope formula

Which is the most logical order of statements and reasons for the proof? (5 points)

III, I, IV, II, V
III, V, II, IV, I
III, IV, I, II, V
I, IV, III, V, II

Answer 2

Anybody want to help?
No?

Ok I will

Answer 3

@ItryMath
What did you get?

Answer 4

i got C

Answer 5

It would B
III, V, II, IV, I

Check it again please!

Answer 6

hold on let me check

Answer 7

i dont understand

Answer 8

Firstly he specift the coordinates of the two points >>>>>>>>> III

oK?

Answer 9

ok

Answer 10

Can you kindly respond more faster, please?

Answer 11

Then he calculated the slope for each, and found that they are equal>>>V
ok?

Answer 12

okay

Answer 13

Then he conclude that they are parallel as their slopes are the same!>>>>>II

Do you follow?

Answer 14

@ItryMath

Answer 15

yes im just look in the book

Answer 16

next?

Answer 17

length of the segment ?

Answer 18

Correct!

which is IV then I

got it?

Answer 19

okey i get it thanks!

Answer 20

Thank you for learning!
I appreciate!

Answer 21

Any more questions?