18-2: Using Similarity Criteria
Objectives:
1.
To find missing measures in similar polygons
Assignment:
• P. 264: 4, 5
• P. 271-272: 2-8
• Challenge Problems

Objective 1
You will be able to find missing measures in similar polygons

Indirect Measurement
Indirect measurement involves measuring distances that cannot be easily measured directly.
This often involves using properties of similar triangles.

Thales
The Greek mathematician
Thales was the first to measure the height of a pyramid by using geometry. He showed that the ratio of a pyramid to a staff was equal to the ratio of one shadow to another.

Example 1
If the shadow of the pyramid is 576 feet, the shadow of the staff is 6 feet, and the height of the staff is 5 feet, find the height of the pyramid.

Example 2
Explain why Thales’ method worked to find the height of the pyramid?

Example 3
If a person 5 feet tall casts a 6-foot shadow at the same time that a lamppost casts an
18-foot shadow, what is the height of the lamppost?

Investigation 2
What if you decide to indirectly measure a height on a day when there are no shadows?
The following GSP
Animation will help you discover an alternate method of indirect measurement using a mirror.

Example 4
Your eye is 168 centimeters from the ground and you are 114 centimeters from the mirror.
The mirror is 570 centimeters from the flagpole. How tall is the flagpole?

Example 5
Find the values of 𝑥 and 𝑦 .
28
24 x y
24
18

18-2: Using Similarity Criteria
Objectives:
1.
To find missing measures in similar polygons
Assignment:
• P. 264: 4, 5
• P. 271-272: 2-8
• Challenge Problems