1. Triangles have three sides-but how long can those sides be, in relation to each

other? If you have a set of sticks that are aliI, 2, 3, 4, 5, 6, 7, 8, 9, or 10 cm long,

what combinations of sticks can be put together to form a triangle?

a) Use the Geometer's Sketchpad applet "Finding Sides" available on your facilitator's

Fostering Geometric Thinking Toolkit DVD^{1} to explore this question. In the

chart below, list at least five sets of sticks (3 sticks in each set) that form a

triangle and at least five sets of sticks that do not form a triangle.

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^{I}If you do not have access to Geometer's Sketchpad software. you can find a Web-based applet for this problem at

www.geometric-thinking.orglfindin~sides.htm.

b) Now consider a particular set of triangles-triangles with perimeter 12. What

sets of three sticks combine to create a triangle with perimeter 12? Use the

Geometer's Sketchpad file to explore this question. In the chart below, list at

least five sets of sticks (3 sticks in each set) that form a triangle of perimeter

12 and at least five sets of sticks that do not form a triangle of perimeter 12.

c) Are there other sets of three side lengths not shown on the applet that would

create a triangle with perimeter 12? If so, what are they? If not, why not?

2. Sandy's teacher gave her 7 sticks and asked her to try to make triangles using

only those 7 sticks. Sandy tried every possible combination of 3 sticks, but none

of the combinations formed a triangle. All 7 sticks in Sandy's pile had integer

lengths (i.e., the lengths did not include any fractions of units). It is possible

that Sandy had more than one stick of the same length. Given what you learned

about the side lengths that will form a triangle in question 1:

a) Could the longest of Sandy's 7 sticks be 12 cm? Support your answer with a

convincing mathematical argument.

b) Could the longest of Sandy's 7 sticks be 13 cm? Support your answer with a

convincing mathematical argument.

c) Could the longest of Sandy's 7 sticks be 14 cm? Support your answer with a

convincing mathematical argument.

3. If Sandy had 10 sticks that were all integer lengths and still couldn't form any

triangles using those sticks. what is the shortest that the longest of those sticks

could be? Explain why you think the length that you list is the shortest possible

length for the longest of the 10 sticks.