Warm up on triangle angle sum theorem in a simple algebraic context. Went over homework on finding angles in isosceles triangles, then assessed. After assessment, had brief introduction to a new type of line called a median and the point where all 3 medians intersect, the centroid.
Homework
p. 197 #17-22 [CO-C10b]
Resources
centroid concept: link
video example just like the homework (made by me :)) LINK
Passed back assessments and project rubrics. Made the centroid of a triangle and demonstrated how it is the point where the 3 medians of a triangles intersect and is the center of mass for the triangle, so the balancing point in one sense. Saw how center of mass affects a linear object of uniform density with a video from the Intl Space Station and extended the idea of midpoint being the center of mass to centroid being the center of mass, bringing us the centroid formula, which is just the average of the 3 x-coordinates and 3 y-coordinates. Worked an example, then shifted to altitudes. Saw how altitudes cross in a point called the orthocenter, which falls on the same line as the centroid and circumcenter. Finally made foldable with information and examples on all 4 major triangle centers (circumcenter, incenter, centroid, orthocenter).
Notes from board
Homework
p. 202 #9, 13-16, 20, 21
Resources
demonstration of centroid formula (help for 13-16): LINK
check foldable from class for help with others
Warm up dealt with an algebraic approach to triangle median lengths and centroids. Spent most of class in jigsaw groups, where 1 person at each table focused on either circumcenter, incenter, centroid, or orthocenter with a common triangle at each table. Then put them simultaneously onto a single large canvas per table, revealing the 4 major points of concurrency as well as the Euler line hidden within each triangle.
Homework:
take notes on this video: direct link [Also! A QUIZLET with these definitions! link]