On Tuesdays I upload an update of what we did in math for the week.

RightStart Geometry:

Lesson 53 Connecting Midpoints in a Triangle

This ended up being the only math lesson done all week (due to a field trip and then illness). It ended up being a doozy, though.

The worksheet has a triangle on it; the student is supposed to find the midpoint of each side of the triangle, then connect the midpoints. Kid1 quickly found the midpoint of the base, next found the midpoint of one of the legs, then collapsed into tears of frustration trying to find the midpoint of the other leg.

She cried for help (in a very specific way -- the directions to parents say that the student should ask

*specific*questions, not just a general “I don’t get it”). I, of course, have no memory of how to find the midpoint of

*anything*other than just measuring the line and dividing by two. I absent-mindedly roated the T-square around while contemplating how to approach the problem. Kid1 huffily pointed out that the T-square is to remain in the same direction through all the work, and that had been taught in one of the early lessons (subtext: get a clue, Mom). Then I had the brilliant notion to ask her to show me everything she’d done so far.

“Well, I found the midpoint of the base, then of this line....”

“No, show me step by step. Be specific.”

She showed me. Aha, now I sort of remember how to do this. It’s a matter of using the 45 angle, dropping down to a line parallel to the base, make a new triangle, then drawing a line back from the apex of that triangle back to the line you’re bisecting. Kid1 had neglected that last step of going from the apex back up to the line; actually, I wasn’t sure this was exactly how you’re supposed to do it, but it appeared to work.

Next she connected the midpoints. She was supposed to discuss whether lines in the new triangle were parallel to the lines in the outer triangle. “Some lines seem to be parallel; you can check it with your drawing tools.” The book cheerfully prompted, “If you’ve forgotten how, look back to Lesson 33.” We dutifully turn to Lesson 33, and discover that it’s about Area of a Triangle. Huh?

I know there’s some way to use your drawing tools to figure out parallel lines, but my memory of it is as hazy as my memory of how to bisect a line segment. I suggest she eyeball it. Actually, her lines are a bit off due to the imprecision of her work. I suggest she just go with it because it makes sense to me (some sort of distant memory of 10th grade geometry, I guess) plus I peeked at the answer page.

The rest of the lesson went okay -- just a matter of figuring ratios. Well, it went okay once we had a quick review of what ratios are.

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