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Triangles Presentation Transcript

  • 1. GEOMETRY Triangles
  • 2. We can classify triangles by their sides: Scalene – no sides are the same length
  • 3. We can classify triangles by their sides: Isosceles – two sides are the same length (Base angles are also equal)
  • 4. We can classify triangles by their sides: Equilateral – all sides are the same length (All angles are also equal and 60 °)
  • 5. We can classify triangles by their angles: Acute angles – all angles are acute
  • 6. We can classify triangles by their angles: Obtuse angles – one angle is obtuse
  • 7. We can classify triangles by their angles: Right angled – one angle is a right angle
  • 8. PROOF – Angle Sum of a Triangle Construction: Draw a line DE parallel to AC. D E ﮮ ACB = ﮮ CBE = z ° (Alternate angles on AC║DE) z ° ﮮ BAC = ﮮ ABD = y ° (Alternate angles on AC║DE) y ° ﮮ DBA + ﮮ ABC + ﮮ EBC = 180 ° y° + x° + z° = 180° (Angles on a straight line add to 180 ° ) Therefore ﮮ BCA + ﮮ ABC + ﮮ BAC = 180 °
  • 9. PROOF – Exterior Angle of a Triangle Construction: Draw CE parallel to AB. ﮮ BAC = ﮮ ECD = y ° (Corresponding angles on AC║DE) ﮮ ABC = ﮮ BCE = x ° (Alternate angles on AC║DE) ﮮ BCD = ﮮ ABC + ﮮ BAC z° = x° + y° D E z °