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 explain why or why not.
Measurements of each object:
pencil #1: 8 inches
pencil #2: 7 inches
pencil #3: 8 inches
The three objects that could represent the sides of a triangle are pencil #1 (8 inches), pencil #2 (7 inches), and pencil #3 (8 inches).
To determine if these three pencils can form a triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let's consider pencil #1 and pencil #2. Their combined lengths are 8 inches + 7 inches = 15 inches. Since 15 inches is greater than the length of pencil #3 (8 inches), pencil #1 and pencil #2 can form a triangle with pencil #3.
Similarly, let's consider pencil #1 and pencil #3. Their combined lengths are 8 inches + 8 inches = 16 inches. Since 16 inches is greater than the length of pencil #2 (7 inches), pencil #1 and pencil #3 can also form a triangle with pencil #2.
Finally, let's consider pencil #2 and pencil #3. Their combined lengths are 7 inches + 8 inches = 15 inches. Again, since 15 inches is greater than the length of pencil #1 (8 inches), pencil #2 and pencil #3 can form a triangle with pencil #1.
Therefore, based on the Triangle Inequality Theorem, we can conclude that the three pencils can indeed form a triangle.
rewrite if a 7th grader wrote it
To see if these three pencils can make a triangle, we need to remember a rule called the Triangle Inequality Theorem. It says that the sum of the lengths of two sides of a triangle must be bigger than the length of the third side.
So, when we add the lengths of pencil #1 and pencil #2, we get 8 inches + 7 inches = 15 inches. That's more than the length of pencil #3 (8 inches), so we can make a triangle using those two.
Next, if we add the lengths of pencil #1 and pencil #3, we get 8 inches + 8 inches = 16 inches. That's bigger than the length of pencil #2 (7 inches), so we can make a triangle with these two as well.
Lastly, adding the lengths of pencil #2 and pencil #3 gives us 7 inches + 8 inches = 15 inches. That's also bigger than the length of pencil #1 (8 inches), so we can make a triangle with those two.
So, according to the Triangle Inequality Theorem, yes, we can make a triangle using these three pencils.