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 11.3
h
6 ft.
21 ft.
9 ft.
ℎ
21 𝑓𝑡.
=
6𝑓𝑡.
9 𝑓𝑡.
ℎ ∗ 6 𝑓𝑡.
21 𝑓𝑡.∗ 6 𝑓𝑡.
=
6 𝑓𝑡.
9 𝑓𝑡.
ℎ = 14 𝑓𝑡.
JRLeon
Geometry Chapter 11.3
HGSH
Lesson 11.3
ℎ
8 𝑐𝑚
=
6 𝑐𝑚
10 𝑐𝑚
ℎ ∗ 6 𝑐𝑚
8 𝑐𝑚 ∗ 6 𝑐𝑚
=
6 𝑐𝑚
10 𝑐𝑚
ℎ = 4.8 𝑐𝑚
JRLeon
Geometry Chapter 11.3
HGSH
Lesson 11.3
JRLeon
Geometry Chapter 11.3
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 11.4
HGSH
Lessons 11.3 – 11.4
Classwork:
11.3- Pg. 579 – Problems 4-12
Homework:
11.3- Pg. 599 – Problems 1 through 5
11.4- Pg. 605 – Problems 1 through 14
JRLeon
Geometry Chapter 11.3-11.4
HGSH
Lessons 11.3 – 11.4
JRLeon
Geometry Chapter 11.3-11.4
HGSH
Lessons 11.3 – 11.4
JRLeon
Geometry Chapter 11.3-11.4
HGSH
Lessons 11.3 – 11.4
JRLeon
Geometry Chapter 11.3-11.4
HGSH
Lessons 11.3 – 11.4
Homework: 11.3- Pg. 599 – Problems 1 through 5
Homework: 11.4- Pg. 605 – Problems 1 through 14
JRLeon
Geometry Chapter 11.3-11.4
HGSH