Fundamental Ideas
Triangles
Triangles can be classified either according to their sides or according to their angles. All of each may be of different or the same sizes; any two sides or angles may be of the same size; there may be one distinctive angle.
The types of triangles classified by their sides are the following:
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Equilateral triangle: A triangle with all three sides equal in measure. In Figure 1 , the slash marks indicate equal measure.
Figure 1 Equilateral triangle.
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Isosceles triangle: A triangle in which at least two sides have equal measure (Figure 2 ).
Figure 2 Isosceles triangles.
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Scalene triangle: A triangle with all three sides of different measures (Figure 3 ).
Figure 3 Scalene triangle.
The types of triangles classified by their angles include the following:
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Right triangle: A triangle that has a right angle in its interior (Figure 4 ).
Figure 4 Right triangle.
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Obtuse triangle: A triangle having an obtuse angle (greater than 90° but less than 180°) in its interior. Figure 5 shows an obtuse triangle.
Figure 5 Obtuse triangle.
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Acute triangle: A triangle having all acute angles (less than 90°) in its interior (Figure 6 ).
Figure 6 Acute triangle.
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Equiangular triangle: A triangle having all angles of equal measure (Figure 7 ).
Figure 7 Equiangular triangle.
Because the sum of all the angles of a triangle is 180°, the following theorem is easily shown.
Theorem 27: Each angle of an equiangular triangle has a measure of 60°.
