Midpoints and Congruent Segments - Problem 2
Using what we know about a midpoint we can apply it to a difficult problem and actually it’s not that difficult if you just draw a picture which is one of your problem solving strategies. If ab is equal 20 and c is the midpoint of line segment ab.
I’m going to stop right there and I’m just going to draw my line segment ab. So I’ve drawn my line segment ab and I know that this point c is the midpoint. Now I’m going to mark that ac and cb are congruent because we know that c by definition has to divide that line segment into two congruent pieces.
Next it says d is the midpoint of ac. So taking that line segment ab we divide it in half, and I’m going to divide it in half again and we know that half of ½ is a ¼. So we’ve got point d which is the midpoint of c, and notice I used a different number of markings than I did over here. Find ad.
So what I’m going to do is I’m going to say well I know this whole distance right here is 20 units. I don’t know what the units are here so I’m just going to guess that that’s going to be units. If ac is half of ab, we know that this right here has to be 10, line segment cb. We know that this line segment right here has to be 10 because they’re congruent and if we divide that in half again we know that ad is 5. So find ad. Ad is 5 units.
The key to this problem is drawing a picture and making sure that you know where your midpoints are.