JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 (603) Suppose I wanted to determine the height of a flag pole, but I did not have the tools necessary. Even.

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Presentation transcript:

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 (603) Suppose I wanted to determine the height of a flag pole, but I did not have the tools necessary. Even if I cannot measure the height of the flag pole directly, I can use a method known as shadow reckoning.

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 In shadow reckoning, we use the height of two objects and the length of their shadows to form similar triangles. The reasoning behind this method is that the objects will cast shadows that are proportional to their heights. The triangles which are formed will have the same angles and therefore they will be similar.

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 Suppose we measured the length of the flag pole’s shadow to be 10 feet, my height to be 5.5 feet, and my shadow’s length to be 1.1 feet. What is the length of the flagpole? Now I need to set up a proportion comparing the flag pole’s height and the length of its shadow to my height and the length of my shadow.

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3 To find the height of the flag pole I need to take the cross product of this comparison and then solve for the height of the flag pole.

JRLeon Geometry Chapter 11.3 HGSH Lesson ft. 6 ft. h 21 ft.

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3

JRLeon Geometry Chapter 11.3 HGSH Lesson 11.3

JRLeon Geometry Chapter 11.4 HGSH Lessons 11.4 (598) There is more to similar triangles than just proportional side lengths and congruent Angles. For example, there are relationships between the lengths of corresponding altitudes, corresponding medians, or corresponding angle bisectors in similar triangles. Now we’ll look at another proportional relationship involving an angle bisector of a triangle.

JRLeon Geometry Chapter 11.4 HGSH Lessons 11.4

JRLeon Geometry Chapter 11.4 HGSH Lessons 11.4

JRLeon Geometry Chapter 11.4 HGSH Lessons 11.4 Now let’s look at how you can use deductive reasoning to prove one part of the Proportional Parts Conjecture.

JRLeon Geometry Chapter 11.4 HGSH Lessons 11.4

JRLeon Geometry Chapter 11.4 HGSH Lessons 11.4

JRLeon Geometry Chapter HGSH Lessons 11.3 – 11.4 Classwork: Pg. 579 – Problems 4-12 Homework: Pg. 599 – Problems 1 through Pg. 605 – Problems 1 through 14

JRLeon Geometry Chapter HGSH Lessons 11.3 – 11.4

JRLeon Geometry Chapter HGSH Lessons 11.3 – 11.4

JRLeon Geometry Chapter HGSH Lessons 11.3 – 11.4

JRLeon Geometry Chapter HGSH Lessons 11.3 – 11.4 Homework: Pg. 599 – Problems 1 through 5 Homework: Pg. 605 – Problems 1 through 14