Triangle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

Triangletriangle 2triangle 1

  • All triangles have three angles.
  • All triangles have three sides.
  • The sum of all angles of a triangle always equal \(180^\circ\).          \( x^\circ \;+\; y^\circ \;+\; z^\circ = 180^\circ  \)
  • Sides:  \(a\),  \(b\),  \(c\)
  • Angles:  \(A\),  \(B\),  \(C\)
  • Height:  \(h_a\),  \(h_b\),  \(h_c\)
  • Median:  \(m_a\),  \(m_b\),  \(m_c\)  -  A line segment from a vertex (coiner point) to the midpoint of the opposite side
  • Angle bisectors:  \(t_a\),  \(t_b\),  \(t_c\)  -  A line that splits an angle into two equal angles
  • Perimeter:  \(P\)
  • Semi-perimeter:  \(s\)  -  One half of the perimeter
  • Area:  \(K\)
  • Inradius of triangle:  \(r\)
  • Outradius (circumcircle) of triangle:  \(R\)   

Types of Triangles

Right Isosceles Triangleright isosceles triangle 1

  • One side of a right isosceles triangle is 90° and two angles are equal.

 

 

 

 

 

Right Triangleright triangle 1

  • One side of a right triangle is 90°, the other two angles are unequal and no sides are equal.

 

 

 

 

 

Equilateral Triangleequilateral triangle 1

  • An equilateral triangle is when all three angles are equal.
  • A equilateral triangle is a polygon.

 

 

 

 

Isosceles Triangleisosceles triangle 1

  • An isosceles triangle is when two sides are equal and two angles are equal.

 

 

 

 

 

Acute Triangleacute triangle 1

  • An acute triangle is when all three angles of the triangle are less than right angles.
  • An acute triangle is a oblique triangle.

 

 

 

 

Obtuse Triangleobtuse triangle 2

  • An obtuse triangle is when one of the three angles is greater than a right angle.
  • An obtuse triangle is a oblique triangle.

 

 

 

 

Scalene Trianglescalene triangle 3

  • An scalene triangle is when no sides and angles are equal.

 

 

 

 

Tags: Equations for Triangle