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these are a bit tricky. The first thing to do is read the theorem. What facts do they want to show?
I'm not sure what you mean...
At the top of the page, it gives a theorem. What does the theorem say?
The segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
But what does that mean? I don't understand the theorem itself...
yes. there are two things the theorem says: 1) segment is parallel to the 3rd side 2) 1/2 its length those are the facts you have to prove. So those 2 facts should come at the end of the proof
But what does that mean? |dw:1359066662711:dw|
Do you understand ? the segment connects the middle of each leg now back to the problem. Can you figure out which statements are the 2 facts the theorem has to prove? which statements mean 1) segment is parallel to the 3rd side 2) 1/2 its length
Let's answer one at a time Of the statements I, II, III, IV, and V which one says segment is parallel to the 3rd side
yes. So statement I is one of the things that has to be proved. That means it can't be first. You don't start a proof by writing the conclusion first. Let's try to figure out what statement comes BEFORE statement I Statements IV and V talk about lengths, so I think those are for the other statement to prove. We will get to those later. Now of the statements that are left: II and III which one would you use to say you have parallel lines (proving statement I)
In other words, look at the reason for statement I. which of the other statements support that reason ?
3 because it talks about having equal slopes?
yes, so we have (so far) III, I if any of the answer choices have I before III we should cross it off the list
now look a the reason for statement III: by the slope formula do you know what the formula is for finding the slope? what do you need to know to use the slope formula?
remember slope is change in y divided by change in x
y=mx+b you have to know the y intercept and I forgot the other part
that is the equation for a line in slope-intercept form. to find the slope m, you find the change in y divided by the change in x you need two points (x1,y1) and (x2,y2) so you can find (y2-y1)/(x2-x1) which of the statements gives you 2 points so you can find the slope?
Yes, now we have II, III, I we have to do the statements in that order. II gives us points that we use in III to find the slopes that we use in I to say the slopes are = so if any of the answers has II after either III or I, you should cross it off. Have you done that yet?
So it's D? Thanks!
double check. D has II at the end. But we know the order has to be II, III, I So I would cross off D
look for a choice that II, III, I in that order (and ignore IV and V)
my bad, i meant to say B (typo)
OK, I was wondering how you could pick D. notice we did not have to figure out the order of statements IV and V but you should know that V is the conclusion: it says the segment is 1/2 the length of side AC. A conclusion comes last. so the other statements have to be in the order IV, V
Okay, can you help me with another?
@phi can you help with another?
ok post it