After welcome back, worked through as review, a simple sun-shadow problem involving similar triangles. Something like it is linked here. Then dove into extending the idea of similar triangles into overlapping figures which developed the Triangle Proportionality Theorem. Also showed how lines can be proven parallel by using this theorem in reverse (converse). See videos in resources for more clarification. (SRT-B4b)
Then reviewed Pythagorean Theorem and worked problems using it. Looked at similarity WITHIN right triangles. Showed that since the Pythagorean theorem only applies to right triangles, having the 3 side lengths of a triangle can allow you to determine if it is a right triangle or not. (This is the converse, since you are working backwards.) See below for an example of how to use it to help with the final problem in the hw. (SRT-B4c).
Hw:
p.270 #16 (SRT-B4b)
p. 286: #5, 6, 13 (SRT-B4c)
Resources:
NUMBER FIVE ON HW: Not familiar with baseball? Here is a baseball diamond; the problem in the book tells you the lengths of the sides of the square. The person is throwing the ball from 3 feet outside the square, directly below home plate all the way across the field to 2nd base. The question is how long is the throw?
Triangle proportionality: great video with intro, examples, and even proof: link
proving lines parallel in proportional triangles: link
Similarity within right triangles: this video is like what we did in class: link
Converse of Pythagorean theorem: how to figure out if a triangle is right or not: link
Warm up on Pythagorean theorem. Went over homework in small groups. Then discovered similarity within right triangles during discovery activity. Worked through geometric mean formula, did a few examples, and then saw an application in a real world setting involving decision making and a few simple statistics. (SRT-B5d)
Notes here
Notes here for A Day
Homework:
p. 281: #2c, 5, 8, 9
SRT-B5d
Resources:
basics of right triangle similarity and geometric mean (recap of lesson) link
writing a similarity statement (#2c on hw) link
using geometric mean and similarity to solve problems (#5): link
more geometric mean, given altitude (#8 in hw): link, occurs at 4:26 into video