00:02
Okay, we've got a line segment, line segment df, and we're given that e is the midpoint of df, and we've got to prove that 2de equals df.
00:19
So let's make our two -column proof.
00:28
We've got our statements and our reasons.
00:34
So, first statement, we always start with what's given, so i can say e is the midpoint of df, and the reason that was given.
00:55
Okay, the second statement is that de is congruent to ef, and the reason for that, that's the definition of midpoint.
01:15
That's what it means to be a midpoint.
01:18
You create two congruent segments.
01:26
Then the statement after that is that the measure of de, subtle difference here, equals the measure of ef.
01:39
So, for segments, the distinction between congruence and equality is very subtle.
01:58
So saying they're congruent means they're the same shape.
02:02
Saying their measures are equal means that those numbers, the numbers associated with the measures are equivalent, and the reason for that, it's just a definition.
02:15
It's the definition of segment congruence.
02:26
We can say two segments are congruent if their measures are equal.
02:35
Okay, then we're given the reason for the next statement is the segment addition postulate, which says that two smaller segments that make up a bigger segment, like we've got here, if we add the measures of the smaller ones, so i could do de plus ef, then i will get the measure of the bigger one, which is df.
03:21
So our next statement after that is de plus de equals df.
03:39
And you can see it's almost identical to the statement above it, except for instead of an ef here, we've got a de.
03:51
Let me underline de in red.
03:55
And then if you look up a statement before that, we know that de equals ef...