The Pythagorean Theorem is a super handy tool for telling the differences between three types of triangles: right, acute, and obtuse. Let’s break it down!
Right Triangles: A right triangle has one angle that is exactly 90 degrees. The Pythagorean Theorem tells us that in a right triangle, the sides relate like this: (a^2 + b^2 = c^2). Here, (c) is the longest side, called the hypotenuse. If this equation is true, then you have a right triangle!
Acute Triangles: An acute triangle has all angles less than 90 degrees. For these triangles, the relationship changes to: (a^2 + b^2 > c^2). This means that when you add the squares of the two shorter sides, it will be greater than the square of the longest side.
Obtuse Triangles: An obtuse triangle has one angle that is greater than 90 degrees. For these triangles, the relationship looks like this: (a^2 + b^2 < c^2). This tells us that the sum of the squares of the two shorter sides is less than the square of the longest side!
Knowing these relationships can make you better at geometry and help you think mathematically. Get excited to show off your new skills!
The Pythagorean Theorem is a super handy tool for telling the differences between three types of triangles: right, acute, and obtuse. Let’s break it down!
Right Triangles: A right triangle has one angle that is exactly 90 degrees. The Pythagorean Theorem tells us that in a right triangle, the sides relate like this: (a^2 + b^2 = c^2). Here, (c) is the longest side, called the hypotenuse. If this equation is true, then you have a right triangle!
Acute Triangles: An acute triangle has all angles less than 90 degrees. For these triangles, the relationship changes to: (a^2 + b^2 > c^2). This means that when you add the squares of the two shorter sides, it will be greater than the square of the longest side.
Obtuse Triangles: An obtuse triangle has one angle that is greater than 90 degrees. For these triangles, the relationship looks like this: (a^2 + b^2 < c^2). This tells us that the sum of the squares of the two shorter sides is less than the square of the longest side!
Knowing these relationships can make you better at geometry and help you think mathematically. Get excited to show off your new skills!