6 Algebra in Geometry

The three angles in a triangle always add up to 180°

So if two angles are known, the third can be worked out                      a+b+c= 180 a+40+75 = 180 a+115 =180 a =180 -115 a =65°

6A Work out the third angle in these triangles.

In the isosceles triangle shown the two equal angles shown are each x°

The neatest way of writing this down is 2x+30 = 180 2x = 180-30 2x = 150 x = 75°

6B Write down an equation in x and solve it to find the size of the marked angles.

One of the most famous mathematical theorems is Pythagoras' Theorem. This states that the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the two shorter sides. This is more clearly shown with a diagram and the formula written algebraically

h²=a²+b²

So to find the length of the hypotenuse or to find the length of a shorter side

         h² = a²+b²					h² = a²+b²

         h² = 6²+8² 					9² = a²+7²

         h² = 36+64 					81 = a²+49

          h² = 100 				          81 - 49 = a²

           h = Ö100 					Ö32 = a

           h = 10cm					    a = 5.66cm

6C Work out the length of the third side of each of these triangles.

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