3.1 and 3.3 Building Triangles and Quadrilaterals

Objective:

The main focus of this problem is to explore what combinations of side lengths allow us to build different types of triangles and quadrilaterals.  In addition, we will determine if a given combination of side lengths forms a unique polygon.

3.1 - Building Triangles

Task A: Building the Triangles.

In this part of the problem, you need to try to build triangles using a variety of different side length combinations.  You will record your work on Labsheet 3.1. For each combination, you need to do the following:

• Try to build the triangle using lego or virtual polystrips.
• If it is possible to build a triangle, make a sketch of the triangle that you built.
• Label and name your sketches with the most appropriate name.
• When building, think of possible ways to make different triangles, these could include changing the order that you attach the sides, or possibly "flexing" the angles.  See what works and what doesn't.

Here are the first four triangle side combinations to try:

• 3, 4, 5
• 2, 4, 8
• 3, 3, 6
• 5, 5, 9

Task B: Looking For Patterns

Complete the three questions from Task B in your squarebook. (P.63)

EXTENSION:

Once you have tested the four combinations that I have given you, create three different sets of side lengths that meet the requirements that I have listed in the table.

3.3 - Building Quadrilaterals

Task A: Building Quadrilaterals

In this part of the problem, you need to try to build quadrilaterals using a variety of different side length combinations.  You will record your work on Labsheet 3.3. For each combination, you need to do the following:

• Try to build the quadrilateral using lego or virtual polystrips.
• If it is possible to build a quadrilateral, make a sketch of the quadrilateral that you built.
• Label and name your sketches with the most appropriate name.
• When building, think of possible ways to make different quadrilaterals, these could include changing the order that you attach the sides, or possibly "flexing" the angles.  See what works and what doesn't.

Here are the first four quadrilateral side combinations to try:

• 8, 8, 10, 10
• 3, 5, 9, 5
• 2, 3, 10, 4
• 6, 10, 3, 5

Here is the virtual polystrip site if you need it:

Task B: Analyzing Quadrilateral Patterns

When you are finished...Answer all of the questions from TASK B (pg. 66)

EXTENSION:

Once you have tested the four combinations that I have given you, create three different sets of side lengths that meet the requirements that I have listed in the table.

HOMEWORK:

1. Complete ALL TASKS from 3.1 and 3.3 described above.
2. 3.1 ACE Problems (1-5) (28)
3. 3.3 ACE Problems (10-14) (29-30)