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How Can You Determine the Type of Triangle Using the Pythagorean Theorem with Given Side Lengths?

To figure out what kind of triangle you have using the Pythagorean Theorem, you need to know a few basics.

The Pythagorean Theorem says that in a right triangle, if you square the lengths of the two shorter sides (called legs) and add them up, you will get the same number as the square of the longest side (called the hypotenuse). The formula looks like this:

a2+b2=c2a^2 + b^2 = c^2

In this formula, c is the longest side.

Now, let's break down the types of triangles you can find:

  1. Right Triangle: If the equation is true (meaning the two sides squared add up to the hypotenuse squared), then it's a right triangle.

  2. Acute Triangle: If the sum of the squares of the two shorter sides is greater than the square of the longest side (so, a2+b2>c2a^2 + b^2 > c^2), it’s an acute triangle. This means all angles in the triangle are less than 90 degrees.

  3. Obtuse Triangle: If the sum of the squares of the two shorter sides is less than the square of the longest side (so, a2+b2<c2a^2 + b^2 < c^2), then it's an obtuse triangle. This means one angle is greater than 90 degrees.

Sometimes, it can be tricky to find which side is the longest. It's very important to clearly label the sides of the triangle first.

Taking your time with your calculations and following each step can help you figure out what type of triangle you have!

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How Can You Determine the Type of Triangle Using the Pythagorean Theorem with Given Side Lengths?

To figure out what kind of triangle you have using the Pythagorean Theorem, you need to know a few basics.

The Pythagorean Theorem says that in a right triangle, if you square the lengths of the two shorter sides (called legs) and add them up, you will get the same number as the square of the longest side (called the hypotenuse). The formula looks like this:

a2+b2=c2a^2 + b^2 = c^2

In this formula, c is the longest side.

Now, let's break down the types of triangles you can find:

  1. Right Triangle: If the equation is true (meaning the two sides squared add up to the hypotenuse squared), then it's a right triangle.

  2. Acute Triangle: If the sum of the squares of the two shorter sides is greater than the square of the longest side (so, a2+b2>c2a^2 + b^2 > c^2), it’s an acute triangle. This means all angles in the triangle are less than 90 degrees.

  3. Obtuse Triangle: If the sum of the squares of the two shorter sides is less than the square of the longest side (so, a2+b2<c2a^2 + b^2 < c^2), then it's an obtuse triangle. This means one angle is greater than 90 degrees.

Sometimes, it can be tricky to find which side is the longest. It's very important to clearly label the sides of the triangle first.

Taking your time with your calculations and following each step can help you figure out what type of triangle you have!

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