Returned Lines and Angles test; error analysis test corrections due next class period. Handed out Chapter 4 Syllabus, available here which includes details about the extra credit project (due Oct 1). More details about that pending. Used private think time to consider the proof of the Exterior Angles Theorem, and then worked some examples to use it.
Homework: p. 227: 4-15, 20, 28-33
Resources: http://www.mathopenref.com/triangleinternalangles.html
http://www.mathopenref.com/triangleextangletheorem.html
Tuesday/Wednesday
A journal entry dealt with explaining the idea of congruence in our own words, as well as methods to determine whether two objects are identical. One way that was presented was placing the two on top of each other and making sure each piece matches the other.
Homework: p. 235: #3-10, 17, 18, 23-25, 31-34
Resources:
http://www.mathopenref.com/congruenttriangles.html
Thursday/Friday
A warm-up check-for-understanding dealt with classifying triangles in 2 ways, matching parts of congruent triangles, and using the exterior angle theorem. This was a classwork grade.
After discussing questions on the homework, we used uncooked spaghetti and cut the sticks into three parts that either did, or did not, form a triangle. We measured the pieces, recorded their values on an anchor chart, and then used private think time to observe any patterns or relationships from the sets of lengths that did work and those that didn't. We arrived at the Triangle Inequality Theorem which states that the sum of two sides of a triangle must be greater than the length of the third side.
We then saw that to find the range of values for a third side in a triangle, the sum and the difference of the two given sides represented the upper and lower bounds, respectively.
Using a kinesthetic activity and an online applet, we also explored the relationship between sides and angles in a triangle. The largest side is located directly opposite the largest angle, and the smallest side is located directly across from the smallest angle.
Examples were worked out of each of these investigations.
Homework: p. 336: 18-31 (all), 42-48 (evens)
Resources:
http://www.mathopenref.com/triangleinequality.html
http://www.mathopenref.com/triangleinequalityconverse.html
http://www.mathopenref.com/trianglesideangle.html