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What Is the Triangle Inequality Theorem and Why Is It Important in Geometry?

The Triangle Inequality Theorem

The Triangle Inequality Theorem is a rule about triangles. It says that for any triangle, if you take the lengths of any two sides, their total length must be greater than the length of the third side.

You can write this rule like this:

  1. a + b > c
  2. a + c > b
  3. b + c > a

Why This is Important in Geometry:

  • Checking Triangle Formation: This rule helps us figure out if three lengths can make a triangle.

  • Learning About Side Relationships: It helps us understand how side lengths are connected to each other.

Example: Let’s say we have three sides with lengths of 3, 4, and 5. We can check the rule by looking at:

  • 3 + 4 > 5 (This is True)

  • 3 + 5 > 4 (This is True)

  • 4 + 5 > 3 (This is True)

Since all of these checks are true, we can say that these lengths can indeed make a triangle!

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What Is the Triangle Inequality Theorem and Why Is It Important in Geometry?

The Triangle Inequality Theorem

The Triangle Inequality Theorem is a rule about triangles. It says that for any triangle, if you take the lengths of any two sides, their total length must be greater than the length of the third side.

You can write this rule like this:

  1. a + b > c
  2. a + c > b
  3. b + c > a

Why This is Important in Geometry:

  • Checking Triangle Formation: This rule helps us figure out if three lengths can make a triangle.

  • Learning About Side Relationships: It helps us understand how side lengths are connected to each other.

Example: Let’s say we have three sides with lengths of 3, 4, and 5. We can check the rule by looking at:

  • 3 + 4 > 5 (This is True)

  • 3 + 5 > 4 (This is True)

  • 4 + 5 > 3 (This is True)

Since all of these checks are true, we can say that these lengths can indeed make a triangle!

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