Building Polygons (Part 2): IM 7.7.7
[url=https://im.kendallhunt.com/MS/teachers/2/7/7/preparation.html]“Building Polygons (Part 2)”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.7.7
- IM 7.7.7 Lesson: Building Polygons (Part 2)
- Practice 7.7.7
- IM 7.7.7 Practice: Building Polygons (Part 2)
IM 7.7.7 Lesson: Building Polygons (Part 2)
At a park, the slide is 5 meters east of the swings. Lin is standing 3 meters away from the slide. Draw a diagram of the situation including a place where Lin could be.
How far away from the swings is Lin in your diagram?
Where are some other places Lin could be?
Use the applet to answer the questions below.
Build as many different triangles as you can that have one side length of 5 inches and one of 4 inches. Record the side lengths of each triangle you build.
Are there any other lengths that could be used for the third side of the triangle but aren't values of the sliders?
Are there any lengths that are values of the sliders but could not be used as the third side of the triangle?
Assuming you had access to strips of any length, and you used the 9-inch and 5-inch strips as the first two sides, complete the sentences:[br][list=1][*]The third side can't be _____ inches or longer.[/*][*]The third side can't be _____ inches or shorter.[/*][/list]
We'll explore a method for drawing a triangle that has three specific side lengths. Use the applet to answer the questions below.
Follow these instructions to mark the possible endpoints of one side:[br][br][list=1][*]For now, ignore segment [math]AC[/math] , the 3-inch side length on the left side 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[/img][br][/*][*]Let segment [math]BD[/math] be the 3-unit side length on the right side. Right-click on point [math]D[/math], check Trace On. Rotate the point, drawing all the places where a 3-inch side could end.[/*][/list][br]What shape have you drawn while moving [math]BD[/math] around? Why? Which tool in your geometry toolkit can do something similiar?[br]
3. Use your drawing to create two unique triangles, each with a base of length 4 inches and a side of length 3 inches. Use a different color to draw each triangle.[br][br]4. Repeat the previous instructions, letting segment [math]AC[/math] be the 3-unit side length.[br][br]5. Using a third color, draw a point where the two traces intersect. Using this third color, draw a triangle with side lengths of 4 inches, 3 inches, and 3 inches. [br][br]What do you notice?
IM 7.7.7 Practice: Building Polygons (Part 2)
In the diagram, the length of segment AB is 10 units and the radius of the circle centered at A is 4 units. Use this to create two unique triangles, each with a side of length 10 and a side of length 4. Label the sides that have length 10 and 4.
Select [b]all [/b]the sets of three side lengths that will make a triangle.
Based on signal strength, a person knows their lost phone is exactly 47 feet from the nearest cell tower. The person is currently standing 23 feet from the same cell tower. [br][list][*]What is the closest the phone could be to the person? [/*][*]What is the furthest their phone could be from them?[/*][/list]
Each row contains the degree measures of two complementary angles. Complete the table.
Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b. Explain or show your reasoning.
Mai’s family is traveling in a car at a constant speed of 65 miles per hour.
At that speed, how long will it take them to travel 200 miles?[br]
How far do they travel in 25 minutes?