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

JRLeon Geometry Chapter 11.3 HGSH

Indirect Measurement with Similar Triangles

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.



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.



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.



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.



Lesson 11.3

h6 𝑓𝑡 .

=21 𝑓𝑡 .9 𝑓𝑡 .

9 ft.

6 ft.

h

21 ft.

h∗6 𝑓𝑡 .6 𝑓𝑡 .

=21 𝑓𝑡 .∗6 𝑓𝑡 .

9 𝑓𝑡 .h=14 𝑓𝑡 .



Lesson 11.3

h6𝑐𝑚

=8𝑐𝑚10𝑐𝑚

h∗6 𝑐𝑚6𝑐𝑚

=8𝑐𝑚∗6𝑐𝑚10𝑐𝑚

h=4.8𝑐𝑚



Lesson 11.3


Lessons 11.4 (598)

Corresponding Parts of Similar Triangles

There is more to similar triangles than just proportional side lengths and congruentAngles. 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.


Lessons 11.4



Lessons 11.4



Lessons 11.4


Now let’s look at how you can use deductive reasoning to prove one part of theProportional Parts Conjecture.


Lessons 11.4



Lessons 11.4


JRLeon Geometry Chapter 11.3-11.4 HGSH

Lessons 11.3 – 11.4

Classwork:11.3- Pg. 579 – Problems 4-12

Similar Polygons / Similar Triangles

Homework: 11.3- Pg. 599 – Problems 1 through 511.4- Pg. 605 – Problems 1 through 14


Lessons 11.3 – 11.4



Lessons 11.3 – 11.4



Lessons 11.3 – 11.4



Lessons 11.3 – 11.4

Homework: 11.3- Pg. 599 – Problems 1 through 5Homework: 11.4- Pg. 605 – Problems 1 through 14


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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