Unit 3 - 6
Key Objectives (from the notes):
- Apply properties of medians, altitudes, and midsegments of a triangle.
- Position figures in the coordinate plane for use in coordinate proofs.
- Prove geometric concepts by using coordinate proofs.
Alright, lesson 6! I can see the end approaching at this point! But first we'll have to learn a bit more...
The topics covered in this lesson were pretty intuitive, but for me, there was some fresh information in there. Here's a very quick, one word summary of the lesson: midsegements. And maybe also coordinate proof. But mainly midsegments.
A midsegment of a triangle is a line segment that connects the midpoints of the legs of said triangle. What that means, by the Triangle Midsegment Theorem, which is one of the theorems we learned about in this lesson, is that it is parallel to the base of the triangle is also half the length of the base. To re-explain what I just discussed in the previous two sentences, here's a picture:
The topics covered in this lesson were pretty intuitive, but for me, there was some fresh information in there. Here's a very quick, one word summary of the lesson: midsegements. And maybe also coordinate proof. But mainly midsegments.
A midsegment of a triangle is a line segment that connects the midpoints of the legs of said triangle. What that means, by the Triangle Midsegment Theorem, which is one of the theorems we learned about in this lesson, is that it is parallel to the base of the triangle is also half the length of the base. To re-explain what I just discussed in the previous two sentences, here's a picture:
As you can see from this example, DE is one of three midsegments of triangle ABC. It bisects both AB and BC, is parallel to AC, and, multiplied by two, equals the length of AC.
And I say three midsegments because there could be two others. If I plotted the midpoint of AC as F, then two other midsegments could be DE and DF. |
As I've stated previously, we did cover coordinate proof in this lesson, as well. We only just lightly brushed on it, though; the skill was painted over much more elaborately in the next lesson. We talked about applying triangle properties on a coordinate grid by utilizing the very, very useful Distance Formula and Midpoint Formula.
The last thing I can say is that we learned how to apply all this midsegment stuff algebraically, bringing x's and y's into each problem.
That about covers it for this lesson.
The last thing I can say is that we learned how to apply all this midsegment stuff algebraically, bringing x's and y's into each problem.
That about covers it for this lesson.