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.
(From Unit 7, Lesson 3.)

Problem 4

How many right angles need to be put together to make:

  1. 360 degrees?
  2. 180 degrees?
  3. 270 degrees?
  4. A straight angle?
(From Unit 7, Lesson 1.)

Problem 5

Solve each equation.

\(\frac17(x+\frac34)=\frac18\)

\(\frac92=\frac34(z+\frac23)\)

\(1.5=0.6(w+0.4)\)

\(0.08(7.97+v)=0.832\)

(From Unit 6, Lesson 8.)

Problem 6

  1.  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.
  2. 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.
(From Unit 4, Lesson 3.)