## Process

**Step 1:**

You will begin by recalling information on congruency of triangles.

These relationships will become very handy when you are going out to identify triangles in the real world. Be sure to have these relationships in your memory when determining how you would like to identify different triangles and when finding relevant triangles to use for your projects

The triangle congruency relationships (postulates) we talked about are:

**Side-Angle-Side (SAS) Congruence Postulate:**

If two sides and the included angle of a triangle are congruent to the corresponding two sides and the included angle in another triangle, then the two triangles are congruent.

**Side-Side-Side (SSS) Congruence Postulate**

If the three sides of a triangle are congruent to the corresponding three sides in another triangle, then the two triangles are congruent.

__Angle-Side-Angle (ASA) Congruence Postulate__

If two angles and the included side of a triangle are congruent to the corresponding two angles and included side in another triangle, then the two triangles are congruent.

**Angle-Angle-Side (AAS) Congruence Theorem**

If two angles and a side opposite one of these two angles of a triangle are congruent to the corresponding two angles and side in another triangle, then the two triangles are congruent.

__Right Triangle (Hypotenuse-Leg) Congruence Theorem__

If the hypotenuse and a leg of a right triangle are congruent to the corresponding hypotenuse and leg in another right triangle, then the two triangles are congruent.

**Step 2:**

Next, you will take these postulates/theorems and find objects in the real world where they are represented.

The following are some areas where you can find useful triangles:

- Architecture
- Nature
- Artwork
- Within the home, school or place of business

These are the steps you MUST take when collecting data for your project:

- Identify triangles in various areas of the real world.
- Measure their sides lengths with a 12-inch ruler and record the data.
- Use a protractor and measure the angles. Record the data. Round to the nearest (0.1) inch. (if some triangles do not add up to 180 degrees, you may have to round the angle measurements)
- Suggestions: Find at least two triangles with similar angle or side measurements
- Take a picture of the "triangle" for your records so you have something to refer back to when creating your project.

Below is a proper representation of a triangle in the real world:

**Step 3:**

Finally, you will take these triangles and their measurements and construct a project that you will represent to the class.

You may work with other people for any help you may need, but this is an individual assignment that you will turn in.

Your project MUST include the following:

- Triangles from various areas of the real world with different representations.
- Visual representations of the triangles, whether they be in photographical or pictorial form.
- Be sure to draw and label the triangles properly, when changing the representation from real-life to a pictorial representation.
- Be creative and make your project organized and easy to comprehend.

You will then present your project to the class.

Be sure to explain not only your triangles but where you found them, their classification (isosceles, scalene, equilateral) and the difference or similarities in their angle measurements.

This presentation will also be graded on the terminology you use, so be sure to use higher level vocabulary when describing your triangles.

Your classmates will be given the opportunity to ask any questions if they need to, so be able to describe your representations properly.

Make sure you presentation includes the following:

- Speak in a clear, loud voice for all students to hear.
- Identify your triangles with correct terminology.
- Be able to describe the location in which you found the triangle.
- Use higher order thinking and be able to represent the triangles in a variety of ways (pictorially, photographically, concretely) using terminology you have learned throughout the semester.

This project will allow you to correctly identify that triangles are represented in the real-world.