Triangles

Triangles are polygons with three sides.

Definitions
Types of Triangles
Properties of Triangles

 Definitions

  • A vertex of a triangle is the intersection of two sides.
  • A median is a line from a vertex to the mid-point of the opposite side.
  • An altitude is a line from a vertex that meets the opposite side at an angle of 90°.
  • Two triangles are congruent if they have exactly the same size and shape.

 

Types of Triangles

  • An acute-angled triangle contains no angles greater than 90°.

    e.g. Y10_Triangles_02.gifA, Y10_Triangles_02.gifB and Y10_Triangles_02.gifC are all acute angles.

Y10_Triangles_01.gif
  • A right − angled triangle contains an angle of 90°.

    e.g. Y10_Triangles_02.gifA = 90o Y10_Triangles_03.gif

  • An obtuse − angled triangle contains an angle between 90°and 180°.
Y10_Triangles_04.gif

 

  • A scalene triangle contains three sides unequal in length. All angle sizes are different.
  • An isosceles triangle is one in which two of the sides and their opposite angles are equal.

Symmetry of Triangles

An isosceles triangle has one axis of symmetry.

Y10_Triangles_05.gif

axis of symmetry

e.g. sides: a = b

angles: Y10_Triangles_02.gifA = Y10_Triangles_02.gifB

 

An equilateral triangle is one in which all three sides are of equal length and each interior angle is 60°.

An equilateral traingle has three axes of symmetry.Y10_Triangles_06.gif

e.g. sides: a = b = c

angles: Y10_Triangles_02.gifA =Y10_Triangles_02.gifB =Y10_Triangles_02.gifC

 

WallPattern.JPGProperties of Triangles

  • The interior angles of a triangle always add up to 180°.
  • An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
  • The exterior angles of a triangle always add up to 360°.
  • The smallest angle of a triangle is opposite the smallest side.
  • The largest angle of a triangle is opposite the largest side.

    w = x + y

Y10_Triangles_07.gif

Click here to test your knowledge of the properties of quadrilaterals and triangles.