**Science Fair Survival Guide**

### Problem

What is a triangle?

### Materials

- Scissors
- Ruler
- 3 plastic drinking straws
- 3 small paper clips

### Procedure

- Cut a 4-inch (lO-cm) piece from each straw.
- Open each paper clip as shown in the diagram.
- Insert one bent end of each paper clip into the end of each straw piece. Adjust the angle of the bent paper clip if needed.

### Results

You have made a figure with three straight sides joined only where the sides meet.

### Why?

The figure is an example of a polygon. A **polygon** is a **closed figure** (a geometric figure that begins and ends at the same point) formed by three or more line segments that are joined only where the ends of the line segments meet. Each of these endpoints is connected to only two line segments. A polygon made of three sides is called a **triangle**. The sum of the angles created by the three sides is always 180 degrees. Triangles can be identified according to how many, if any, of their sides are **congruent** (the same). The triangle made in this experiment has three congruent sides and is called an **equilateral triangle**.

### Let's Explore

- A triangle with two congruent sides is called an
**isosceles triangle**. Repeat the experiment, making two pieces of straw longer or shorter than the third piece, to make an isosceles triangle. - No sides of a
**scalene triangle**are congruent. Repeat the original experiment, making each piece of straw a different length, to make a scalene triangle.**Science Fair Hint**: Prepare a poster using the three different triangle models: equilateral, isosceles, and scalene. Use the poster as part of a project display.

### Show Time!

*A*=^{1}/2×*b*+ *i* – 1

This is read: Area (*A*) equals one-half times *b* (the number of nails on the perimeter, or outer boundary, of the triangle) plus *i* (the number of nails inside the triangle) minus 1. For example, for the obtuse triangle in the diagram, you would find the area by the following steps:

Multiply the first two numbers: ^{1}/_{2} × 4 = 2

Add 2 to the product: 2 + 2 = 4

Subtract 1 from the sum: 4 – 1 = 3

*The area 0/ the obtuse triangle is equal to 3 squares on the geoboard.*

- Use the following steps to build a geoboard:
**acute triangle**All angles measure less than 90°.**right triangle**One angle measures exactly 90°.**obtuse triangle**One angle measures greater than 90°.- Ask an adult to hammer twenty-five 3d finishing nails into a block of wood at least 5 inches (12.5 cm) square. The nails should be driven straight, and about half their length should stick out of the wood. Position the nails so that they are 1 inch (2.5 cm) apart in the array shown in the diagram.
- Stretch rubber bands around the nails to create the following triangles which are identified depending on the measure of their angles:
- Label each triangle and display the geoboard.

- The area of the triangles on the geoboard can be calculated by using "Pick's formula," which is written:
- Pick's formula:
- The steps in solving this problem are:

- Display items or drawing of items with triangular shapes, such as a pennant or sail on a boat. Use a
**protractor**(an instrument used to measure angles in degrees) to measure the angles of each triangle. Triangles are named in two different ways: (1) according to how many, if any, of their sides are congruent, and (2) according to the measure of their angles. List both names for each triangular item displayed. Items can be displayed as shown.

For information about using a protractor, see pages 12-13 in *Janice VanCleave's Geometry/or Every Kid* (New York: Wiley, 1994).

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