Math Made Easy

 

Properties of Triangles

The sum of all the angles in a triangle is 180 degrees.

 In the triangle above; x + y + z = 180^o    

Since x = 90,  then y + z = 180 – 90 = 90

 

        The sum of the lengths of any 2 sides is always greater than the length of the 3^rd side.

 

10

x

z

y

8

6

So in the triangle below:

6 + 8 > 10

8 + 10 > 6

6 + 10 > 8

Be sure to check all three combinations if you are given a problem involving this property.

Area = ½ base * height = (base * height) / 2

For example, in the triangle above, the base is 8 and the height is 6. The height is always perpendicular to the base, so with triangles that are not right-angled, you will need to calculate the height. (See next page):

Area of triangle above = ½ base * height

        = ½ 6 * 8 = 24

 

Sample Problem:

Angle at  T = 40, what is the angle at S ? 

    Sum of all angles = 180, R = 90, T = 40, S = 180 - 90 - 40 =50

What is the length of  line ST ? 

    ST² = 6² + 8²  (Pythagoras)

    ST² = 36 + 64 = 100,  ST = 10

What is the area of triangle RST?

    Area = ½ base * height

    Area = ½ (8 * 6) = 24