Quick Start Expectations 1.Come in and sit quietly. 2.Fill in planner and HWRS: 3.Work on Warm-up: If true, provide an example. If false, provide a counterexample (prove that it is not true). 1. True or False: You can make a triangle using any three lengths for sides. 2. True or False: You can make a quadrilateral using any four lengths for sides. Textbook: CMP3 Grade 7 Unit: Shapes and Designs pp , #10-16, 29-31

Notebook Problem 3.3: Building Quadrilaterals 9/30/14 What combinations of side lengths can be used to make a quadrilateral? How many different shapes are possible? (Underline 2 or 3 key words in your question.)

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61012 Yes These sides cannot be used to build a quadrilateral, because is less than No 8810 Yes READ the INSTRUCTIONS CAREFULLY!

Yes, the sum of any three side lengths of the quadrilateral must be greater than the fourth side. Yes, if you can make one quadrilateral from four side lengths, it is often possible to make many different shapes from the same side lengths.

To build parallelograms, including rectangles, the opposite side lengths must be equal. To build squares, including rhombuses, all four side lengths must be equal.

The triangle will hold firm or rigid until the sides themselves buckle.

The quadrilateral will deform quickly into different shapes (unless the connections at the vertices are very tight).

The stress test explains why triangles are used to hold structural shapes firm.

Using a diagonal makes a quadrilateral frame into a rigid figure, because it makes two triangles.

When building triangles and quadrilaterals, each side must be less than the sum of the others. Triangles are rigid figures. Quadrilaterals & other polygons with more than three sides are not. When building a structure, which shape would you use more frequently?

Exit Ticket: What quadrilaterals would be useful in building things? Why? Homework: Textbook: CMP3 Grade 7 Unit: Shapes and Designs pp , #10-16, 29-31