Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
For geometry problems, it is often helpful to draw a picture. Using what we know about midpoints, and given the length of a line segment AB, the midpoint of AB at C, and the midpoint of AC at D, it is possible to find the length of the piece AD.
First, we know that the length of AB is 20. Since C is the midpoint of AB, and midpoints divide line segments into two equal pieces, the length of AC is half of the length of AB, so AC = 10. Then, D is the midpoint of AC, so it divides AC into two equal pieces, meaning that the length of the pieces are half of the length of the segment. So, the length of AD is 5.
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.