can you please help me with geometry? will metal!

Question

anonymous · Answer

Complete the following proof.

Prove: The segment joining the midpoints of two sides of a triangle is parallel to the third side.

anonymous · Answer

https://media.glynlyon.com/g_geo_2012/9/q411a.gif

anonymous · Answer

link to the problem^^^

anonymous · Answer

here's another one: Prove: The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices. https://media.glynlyon.com/g_geo_2012/9/q412a.gif

debbieg · Answer

Well, with that nice sketch provided, you can just find the slope of the segment that joins the midpoints, and find the slope of that 3rd side. If the slopes are the same, then they are parallel. :)

anonymous · Answer

can you show me? @DebbieG

anonymous · Answer

Midpont of AB = ????

anonymous · Answer

x-cordinate of point c = ????

anonymous · Answer

forget those two replys^^^

debbieg · Answer

I'm not sure what you mean. You don't need any midpoints. you need to show that the SEGMENT that joins the midpoints of the 2 sides (MN in the diagram) has the same slope (and hence, is parallel) as the 3rd side (AB).

anonymous · Answer

slope of MN and slope of AB sorry

anonymous · Answer

also M= and n=

debbieg · Answer

So use the points A and B and find the slope of the 3rd side (just use the slope formula, and the coordinates of the points - do you know how to find slope from that?).

And use the points M and N, and the coordinates given, to find that slope.

I'm assuming that's the direction that they want you to go, since you have that lovely diagram in the coordinate plane, and all. :)

debbieg · Answer

given the coordinates of 2 points, do you know how to find the slope? The slope formula?

anonymous · Answer

I don't know how to find slope, can you show me how to get the answer for the first one?

debbieg · Answer

Well, if you don't know the slope formula, I'm wondering now if there is another approach that you are supposed to take.  But slope seems like the easy way to me.

To find the slope m of a line where the points $\large (x_1,y_1)$ and $\large (x_2,y_2)$ are two points on the line, you use:

$\large m=\dfrac{y_2-y_1}{x_2-x_1}$

Are you sure you haven't had that before? Does it look familiar?

debbieg · Answer

And if 2 lines have the same slope, then they are parallel. So showing that these two line segments have the same slope will prove what you're trying to prove.

debbieg · Answer

So first use the coordinates of the points A and B in the slope formula. Then do it again, with the coordinates of M and N.