Angles and Triangles

Bean_Bag_shapes.jpgTriangles are polygons with three sides.

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

e.g. y8_Angles_and_Triangles_01.gifA , y8_Angles_and_Triangles_01.gifB and y8_Angles_and_Triangles_01.gifC are all acute angles.
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A right − angled triangle contains an angle of 90°.

e.g. y8_Angles_and_Triangles_01.gifA = 90°

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An obtuse − angled triangle contains an angle between 90°and 180°. y8_Angles_and_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.
  • An equilateral triangle is one in which all tree of the sides are equal and each angle is 60°.
  • Congruent triangles have the same size and shape.
  • Similar triangles have the same shape.
 

 

Symmetry of Triangles

An isosceles triangle has one axis of symmetry.
 

e.g. sides: a = b

angles: y8_Angles_and_Triangles_01.gifA = y8_Angles_and_Triangles_01.gifB

 y8_Angles_and_Triangles_05.gif

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

An equilateral triangle has three axes of symmetry.

e.g. sides: a = b = c

angles: y8_Angles_and_Triangles_01.gifA = y8_Angles_and_Triangles_01.gifB = y8_Angles_and_Triangles_01.gifC

 y8_Angles_and_Triangles_07.gif

 

Properties of Triangles

The interior angles of a triangle always add up to 180°. a + b + c = 180°
y8_Angles_and_Triangles_08.gif
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. w = x + y y8_Angles_and_Triangles_09.gif
The exterior angles of a triangle always add up to 360°. m + n + p = 360°
y8_Angles_and_Triangles_20.gif
 
  • The smallest angle of a triangle is opposite the smallest side.
  • The largest angle of a triangle is opposite the largest side.