Use the worksheet to record your answers to the Drawing Triangles portfolio activity. When you are finished, save your worksheet with your answers and submit it for a portfolio grade.

Question

Triangles are all around. Understanding triangles is important for work in many areas, not simply math. Triangles are used to build bridges, homes, and other structures. Triangles are used to find distance between geographic locations. In this portfolio, you will demonstrate your understanding of triangles.

Question 1

Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent the sides of a triangle. Can you make a triangle with these three objects? Use the Triangle Inequality Theorem to explain why or why not.

Question 2

Decide if you want to make an acute, obtuse, or right triangle and select three angle measures. How is the Triangle Angle Sum Theorem important for creating triangles? How many triangles can you make with three angle measures? Draw one or more (if possible) examples.

Question 3

Is the Bermuda Triangle really a triangle?

The Bermuda Triangle, sometimes called The Devil’s Triangle, is an imaginary space in the north Atlantic Ocean. Legend famously says ships, aircraft, and people have disappeared when crossing this particular part of the ocean. The diagram shows the region in question.

Answer 1

Drawing Triangles Portfolio Activity

Question 1

Objects Chosen:

1. A stick of length 5 cm
2. A stick of length 7 cm
3. A stick of length 10 cm

Triangle Inequality Theorem:

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's apply this theorem to the chosen objects:

• Side 1 + Side 2 > Side 3:
  \(5 + 7 = 12 > 10\) → True
• Side 1 + Side 3 > Side 2:
  \(5 + 10 = 15 > 7\) → True
• Side 2 + Side 3 > Side 1:
  \(7 + 10 = 17 > 5\) → True

Conclusion:

Since all three conditions of the Triangle Inequality Theorem hold true, you can make a triangle with the chosen objects.

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Question 2

Chosen Angle Measures:

• Angle 1: 50 degrees (acute)
• Angle 2: 60 degrees (acute)
• Angle 3: 70 degrees (acute)

Triangle Angle Sum Theorem:

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees. In this case:

\[ 50 + 60 + 70 = 180 \text{ degrees} \]

How Many Triangles Can You Make with These Angles?

You can only make one unique triangle with these specific angle measures, as the sum is 180 degrees, and they're all acute angles.

Drawings:

1. Acute Triangle

       A
      / \
   B /   \ C
    /_____\

Angle A = 50 degrees, Angle B = 60 degrees, Angle C = 70 degrees

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Question 3

Is the Bermuda Triangle Really a Triangle?

The Bermuda Triangle, also known as the Devil's Triangle, is primarily defined by three points: Miami, Bermuda, and San Juan, Puerto Rico. Geographically, when these points are connected, they form a triangle.

Conclusion:

While it is called the Bermuda Triangle and the area appears to form a triangle when looking at a map, it is important to note that it is not a triangle in the mathematical sense in terms of defined vertices with fixed lengths and angles like a geometrical shape. It is essentially a region in the ocean and is more of a myth than a scientifically proven phenomenon regarding disappearances.

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Summary:

This portfolio activity illustrates the understanding of the properties of triangles, their construction, and real-world representation. The questions encourage exploration of the fundamental aspects of triangles while considering real-world implications.