Published on March 3, 2014
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)?
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
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.
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
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
INVESTIGATION 5 Similar Triangles
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.
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?
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.
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
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
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?
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?
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
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?
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.
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
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?
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?
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