Vocabulary
Scalene Triangle- has no congruent sides.
Isosceles Triangle- at least 2 sides are congruent.
Equilateral Triangle- all sides are (equal) congruent.
Acute Triangle- all the angles are acute.
Obtuse Triangle- has exactly one obtuse angle.
Right Triangle- contains exactly one right angle.
Examples
Classifying Triangles by Sides or Angles
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.
Figure 1 Equilateral triangle
Figure 2 Isosceles triangles
Figure 3 Scalene triangle
Figure 4 Right triangle
Figure 5 Obtuse triangle
Figure 6 Acute triangle.
Figure 7 Equiangular triangle
The types of triangles classified by their sides are the following:
- Equilateral triangle: A triangle with all three sides equal in measure. In Figure 1, the slash marks indicate equal measure.
Figure 1 Equilateral triangle
- Isosceles triangle: A triangle in which at least two sides have equal measure (Figure 2).
- Scalene triangle: A triangle with all three sides of different measures (Figure 3).
The types of triangles classified by their angles include the following:
- Right triangle: A triangle that has a right angle in its interior (Figure 4).
- Obtuse triangle: A triangle having an obtuse angle (greater than 90° but less than 180°) in its interior. Figure 5 shows an obtuse triangle.
- Acute triangle: A triangle having all acute angles (less than 90°) in its interior (Figure 6).
- Equiangular triangle: A triangle having all angles of equal measure (Figure 7).
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°.
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