Lesson 6
Building Polygons (Part 1)
Let’s build shapes.
Problem 1
A rectangle has side lengths of 6 units and 3 units. Could you make a quadrilateral that is not identical using the same four side lengths? If so, describe it.
Problem 2
Come up with an example of three side lengths that can not possibly make a triangle, and explain how you know.
Problem 3
Find \(x\), \(y\), and \(z\).
![Three lines meet to form 6 angles. Clockwise, their measures are 64 degrees, y degrees, z degrees, x degrees, 18 degrees, blank.](https://staging-cms-im.s3.amazonaws.com/8nmmbvb9iBPSFgSobf8fmYbD?response-content-disposition=inline%3B%20filename%3D%227-7.7.A3.new.PP.05.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.A3.new.PP.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T142514Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=317f8807e41b7fe2b0744946bf09ab76261686f7f00cb91e0006c4623dd7662b)
Problem 4
How many right angles need to be put together to make:
- 360 degrees?
- 180 degrees?
- 270 degrees?
- A straight angle?
Problem 5
Solve each equation.
\(\frac17(x+\frac34)=\frac18\)
\(\frac92=\frac34(z+\frac23)\)
\(1.5=0.6(w+0.4)\)
\(0.08(7.97+v)=0.832\)
Problem 6
- You can buy 4 bottles of water from a vending machine for $7. At this rate, how many bottles of water can you buy for $28? If you get stuck, consider creating a table.
- It costs $20 to buy 5 sandwiches from a vending machine. At this rate, what is the cost for 8 sandwiches? If you get stuck, consider creating a table.