Triangles

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Triangles

  1. 1. RAQUEL P. FARIÑAS
  2. 2. 1.Classification: by angles; by sides. 2. Special Lines: Altitude, median, bisector, mediator.TRIANGLES 3. Centres of a triangle: Incentre, circumcentre, centroid, orthocentre.
  3. 3. 1.1. Classifying Triangles by Angles• Acute TriangleA triangle whose three angles are acute is called anacute triangle. That is, if all three angles of a triangleare less than 90°, then it is an acute triangle.
  4. 4. 1.1. Classifying Triangles by Angles• Obtuse TriangleAn obtuse triangle is a triangle that has one obtuseangle.
  5. 5. 1.1. Classifying Triangles by Angles• Right Triangle If one angle of a triangle is 90°, then it is a righttriangle.
  6. 6. 1.1. Classifying Triangles by Angles• Equiangular TriangleIf all three angles of a triangle are 60°.
  7. 7. 1.2. Classifying Triangles by Sides• Equilateral TriangleA triangle with three congruent sides is called anequilateral triangle.
  8. 8. 1.2. Classifying Triangles by Sides• Isosceles TriangleIf a triangle has at least two congruent sides, thenthe triangle is an isosceles triangle.
  9. 9. 1.2. Classifying Triangles by Sides• Scalene TriangleA triangle that has no congruent sides is called ascalene triangle.
  10. 10. 2.1. Altitude• Every triangle has three bases (any of its sides)and three altitudes (heights). Every altitude is theperpendicular segment from a vertex to its oppositeside (or the extension of the opposite side) Three bases and three altitudes for the same triangle.
  11. 11. 2.2. Median• A median in a triangle is the line segment drawnfrom a vertex to the midpoint of its opposite side.Every triangle has three medians. In Figure 5 , E isthe midpoint ofBC . Therefore, BE = EC. AE is amedian of Δ ABC.
  12. 12. 2.3. Angle Bisector/ Bisecting• An angle bisector in a triangle is a segment drawnfrom a vertex that bisects (cuts in half) that vertexangle. Every triangle has three angle bisectors. Infigure below, is an angle bisector in Δ ABC.
  13. 13. 2.4. Mediator• Mediator is the perpendicular bisector of each sideof a triangle.
  14. 14. ?
  15. 15. 3.1. Incentre•Incenter: The three angle bisectors of a trianglemeet in one point called the incenter. It is the centerof the incircle, the circle inscribed in the triangle.
  16. 16. 3.2. Circumcentre• Circumcentre: The three perpendicular bisectorsof the sides of a triangle meet in one point called thecircumcenter. It is the center of the circumcircle, thecircle circumscribed about the triangle.
  17. 17. 3.3. Centroid• Centroid: The three medians (the lines drawnfrom the vertices to the bisectors of the oppositesides) meet in the centroid or center of mass (centerof gravity).
  18. 18. 3.4. Orthocentre• Orthocentre: The three altitudes of a trianglemeet in one point called the orthocenter.

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