Classifying Triangles

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Classifying Triangles
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As you have learned in previous lessons, a
triangle is the simplest polygon, having three
sides and three angles. The sum of the three
angles of a triangle is equal to 180 degrees.
Triangles are classified by sides and by angles.
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Scalene Triangle No equal angles or sides
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Right Angle Triangle One right angle of 90
degrees
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Obtuse Triangle One obtuse angle (more than 90
degrees)
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Isosceles Triangle 2 equal angles and 2 equal
sides (side A side B)
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Equilateral Triangle 3 equal angles and 3 equal
sides (side a side b side c
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Acute Triangle 3 acute angles (less than 90
degrees)
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Just as the rectangle and the circle are very
popular in the real world, so is the triangle!
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You'll find triangles at work bracing a structure
or bridge, racking billiard balls, or holding up
a shelf.
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• Triangles are classified in two general ways
• Sides
• Angles
• First, we'll classify by sides

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• A triangle with three sides of different lengths
  is called a scalene triangle..
• An isosceles triangle has just two equal sides,
  called legs. The third side is called the base.
  The angles that are opposite the equal sides are
  also equal.
• An equilateral triangle has three equal sides. In
  this type of triangle, the angles are also equal,
  so it can also be called an equiangular triangle.
  Each angle of an equilateral triangle must
  measure 60 degrees, since the sum of the interior
  angles of any triangle must equal 180 degrees.

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Now let's classify by angles
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• An acute triangle has three acute angles, or
  three angles with a measure of less than 90
  degrees.
• An obtuse triangle has one angle that is greater
  than 90 degrees. If one of the angles in a
  triangle is a right angle, then the triangle is
  called a right triangle. Notice we draw a square
  at vertex C to show a right angle.

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You can use two labels for a triangle. For
example, triangle MNO is both an acute and an
isosceles triangle. Triangle PQR is an obtuse,
scalene triangle.