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.

Answer 1

@primeralph @koymoi @Easyaspi314@e.cociuba @ehuman

Answer 2

@Easyaspi314

Answer 3

AB = BC becuase of SAS

(BD = BD by identity)

Answer 4

AD = DC because it is marked in the diagram, although I wonder why it is not mentioned in the "Given".

Answer 5

So. A. ok thanks!! and then for the previous question i put, is the answer A? thats what i got. thanks !

Answer 6

It is not A (for the first problem). Because A starts off with DE = 1/2 of AC, but thats what we want to prove. So we are not going to start off with a statement that we want to prove.

Answer 7

Oh, ok so do we start of with The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula. Which makes the answer B

Answer 8

Look at B

Answer 9

Exactly, B is the logical sequence of arguments...we first build up to show that DE is 1/2 of AC...then we build up to finally show that they are parallel.

Answer 10

Ok cool, i have two more questions i need help with if you have any more time, really appreciate it!

Answer 11

For this one i was thinking B

Answer 12

You can post it..but am flooded with many requests.

Answer 13

Yah, im sure you know your stuff!

Answer 14

I'm sure many others will jump in. Post the question.

Answer 15

I posted it, its a few comments back

Answer 16

And i find that many people avoid long geometry questions. @Easyaspi314 your really the only one who answers them

Answer 17

The problem with Abdul (posted above)...the two triangles are similar because of AA, angle-angle similarity.

If you want me to explain this in greater detail, just ask.

Answer 18

Makes sense?

Answer 19

I think i got it. thanks!! then here is the last question if you have the time

Answer 20

By SSS...the sides are congruent in both triangles.

Although I do not like this question at all. It's poorly worded and distracting for the student.

Answer 21

Yah, it was confusing. Thanks so much!! You really helped me.

Answer 22

Welcome.