Got new seats in class. Went over homework, then reviewed/explored similarity within right triangles and how this leads to the geometric mean formula. Worked through some examples of finding internal and external segment lengths by utilizing self-similarity.
Notes from board
Homework
p. 281 #6-9
Resources
basic premise of geometric mean: link
several geometric mean examples worked out: link1 link2
multiple part geometric mean: link
problem like #8: link (at 4:26)
Warm up applied geometric mean, similarity, and pythagorean theorem. Passed out q3 learning targets. Worked through a quick 'lateral thinking' type problem dealing with the Pythagorean theorem and then worked through its proof a variety of ways (see here for method done in class, and here and here for 2 videos watched in class). Then used the Pythagorean theorem to examine the special case of the 45-45-90 triangle.
Notes from board
Q3 learning targets
Homework
p. 289: 4,6,7
p. 299 #2-4
Resources
finding a leg given a hypotenuse and a leg (like #4) : link
finding height of an isosceles right triangle (like #7 except for the area bit): link
finding hypotenuse of 45-45-90: link made by me :) (starts at 3:48)
finding leg of 45-45-90 triangle: link
Warm up dealt with finding legs and hypotenuse of 45-45-90 triangle by recognizing patterns. Another warm up dealt with application of Pythagorean theorem. Went over homework on 45-45-90 and Pythagorean, then did several practice problems ahead of assessment. Took assessment.
Notes from board
Homework:
Watch and take notes on this video: direct link