The document contains instructions and information about using similar triangles to estimate heights and distances that are difficult to measure directly. It discusses using shadows and mirrors to form similar triangles and estimate heights of objects. Measurements are taken of shadows, mirrors, and distances that allow heights to be calculated through properties of similar triangles. Students work through examples estimating heights of buildings using these methods.

1.  The
total land and water area of the United
States is about 3,717,522 square miles. What
percent of this total area is the area of Utah
(2,230 square miles)?

2. Welcome to Pre-Algebra!
Monday:
1. Please have your homework on your desk
and get started on your warm up.
2. Discuss and correct Quiz
3. Complete Application 4
4. Tonight’s Assignment
– Workbook p. 192 - 193

3. Warm-up: Tuesday
• Below is a triangle and its image.
1. Which of these rules was used to make the
image?
(2x,2y)
(x,2y)
(2x, y)
(2x,4y
(4x,2y)
2. Are the triangle and its image similar?
Explain.

4. Welcome to Pre-Algebra!
TUESDAY!
1. Please have your homework on your desk
and get started on your warm up.
2. Correct Application 4 and Workbook p. 193
with your red pen.
3. Partner Assignment
– Due at the end of class
4. Tonight’s Assignment
– Workbook p. 194

5. Welcome to Pre-Algebra!
Wednesday
1. Please have your homework on your desk
and be ready to go over it.
2. Please have your spiral notebook on your
desk.
– 5.1 Use shadows to Find Heights
3. Tonight’s Assignment
– Workbook p. 183 – 184 Stop 1B

6. INVESTIGATION 5
Similar Triangles

7. SIMILAR TRIANGLES

In this investigation, you will see how you can use what
you know about similar triangles to estimate heights and
distances that are difficult or impossible to measure
directly.

8. THINK ABOUT THIS!
As you work on this investigation think about this
question:
Can you explain why each angle of the large triangle
is equal to the corresponding angle of the small
triangle?


9. USING SHADOWS TO FIND
HEIGHTS
If an object is outdoors, you can use shadows to
help estimate its height.
On a sunny day, an object casts a shadow. If you hold
a meter stick perpendicular to the ground, it will
also cast a shadow. The two triangles formed are
similar.


10. SCENARIO
Mr. Anwar’s class is using the shadow method to estimate the
height of their school building.
They have made the following measurements:
Length of meterstick = 1 m
Length of metersticks shadow = 0.2 m
Length of building shadow = 7 m

11. Problem 5.1
A. Use what you know about similar triangles to find the buildings height
from the given measurements. Explain your work.
B. As a class choose a building or other tall object. Work with your
group to estimate the objects height using the shadow method.
Include the measurements your group made, and explain in words
and drawing how you used these measurements to find the objects
height

12. 5.1 FOLLOW UP

1.
2.
As a class we will share the data each group found
for their tall object/building.
Create a line plot of the data.
What does the line plot tell you about the objects
height?

13. Quarter 2: Week 7
WARM-UP 12-13-13
1.
The official size of a basketball court in the NBA is
94 feet by 50 feet. The basketball court in the
school gym is 47 feet long. How wide must it be
to be similar to an NBA court?
2.
Two rectangular desks are similar. The larger one
is 42 inches long and 18 inches wide. The smaller
one is 35 inches long. What is the width of the
smaller desk?

14. Welcome to Pre-Algebra Honors!
Friday: Dec.13, 2013
1. Please have your homework on your
desk and get started on your warm
up.
2. Correct Workbook p. 183 – 184 with
a red pen.
3. Please have out your spiral
notebooks
– 5.2 Using Mirrors to Find Heights

15. THINK ABOUT THIS

As you work on this investigation think about this
question:
Can you explain why each angle of the large triangle
is equal to the corresponding angle of the small
triangle?

16. USING MIRRORS TO FIND
HEIGHTS
The shadow method is useful for estimating
heights, but it only works if you are outside on a
sunny day.
 In this problem we will use a mirror to help estimate
heights. The mirror method works both indoors and
outdoors.


17. SCENARIO

Jim and Qin-Zhong, students in Mr. Anwar’s class, are
using the mirror method to estimate the height of their
school building. They have made the follow
measurements and sketch:
Height from the ground to Jim’s eyes: 150cm
Distance from the middle of the mirror to Jim: 100cm
Distance from the middle of the mirror to the building: 600cm

18. PROBLEM 5.2

1. Use what you know about similar triangles to find the buildings
height from the given measurements. Explain your work.

2. With your group, use the mirror method to estimate the height of
the same object or building you worked with in Problem 5.1. In your
answer, include all the measurements your group made, and explain
in words and drawings how you used the measurements to find the
objects height.

3. How does the height estimate you made using the shadow method
compare with the height estimate you made using the mirror
method? Do you think your estimates for the object’s height are
reasonable? Why or why not?

19. 5.2 FOLLOW UP

1. Work with your teacher to pool the results from
all of the groups. Make a line plot of the data.

2. Compare the line plot of the estimates you made
using the mirror method to the line plot of the
estimates you made using the shadow method.
Which method seems to give more consistent
results?