Triangles:

Source

After the lessons about construction, we move on to the next chapter of geometry.

Today we are going to have a look at triangles.  

Remember that I teach 13 year old learners math, so the work I'm doing is for them to understand.  There are a lot more properties of triangles, but I am starting at the basics. 

Learners need to understand everything from the beginning, otherwise, if they get lost somewhere during the lessons, it is difficult for some of them to catch up again and get on the same level as the rest of the learners.

The angular sum of triangles:

The interior angles of a triangle all adds up to 180 degrees.  We are going to show learners why it adds up to 180 degrees.

• Use a ruler to draw a triangle on a piece of paper.  
• Name each of the angles. In the example it is named a, b and c

• Cut the triangle out and tear it into three pieces so that each piece contains one angle.

Make sure each torn piece of the triangle contains an angle.

• Place the pieces together so that the vertices of the angles meet at one point.

                         

• Fit the angles together.  The angles should form a straight line (180 degrees)
• It doesn't matter in which order it is placed, as long as it can be placed on a straight line.

Learners can draw a new triangle and do the same as above.  They will see that they will get a straight-line angle when placing the 3 angles together. 

The angular sum of a triangle is 180 degrees.

Prior knowledge:

• Different kind of triangles
• Equations

Calculating the third angle of a triangle when 2 of the angles are given.

First we are calculating the angle of a scalene triangle:

We know that all angles added together must give us 180 degrees.

We are going to put it as an equation:

Calculate the unknown angle of the scalene triangle:

a + 46 + 83 = 180      [Interior angles of a triangle]

    a +   129   = 180

                a     = 180 - 129  

                a     =  51 degrees

The unknown angle (a) is equal to 51 degrees.

Calculate the unknown angle of an isosceles triangle:

:

With an isosceles triangle, we know that the 2 angles are equal to each other:

We can calculate it by doing the following:

a + a + 64  = 180     [Interior angles of a triangle]

      2a + 64 = 180

              2a  = 180 - 64  

               2a = 116

The sum of the two angles are equal to 116 degrees.  In the isosceles triangle they just ask "a", not "2a"

Therefore to get the value of a, we have to divide it by 2. (Which will give us 1a)

We also have to divide 116 with 2. (Whatever you do on the left hand side of an equation, you have to do on the right hand side too)

Continuing with the equation:

      2a = 116

2a /2 = 116 /2      [divide on the left and right hand side with 2 to get "a" alone]

     a    = 58 degrees

  

This means that each angle of  "a" will be equal to 58 degrees.  If you add all 3 angles together now, it will give you 180 degrees.

The sum of an equilateral triangle:

"Equal= the same"

Learners should know that all angles of an equilateral triangle will be equal to each other.

To show calculations for an equilateral triangle we do the following:

Each angle is called "a"

Therefore:       a + a + a = 180                 [Interior angles of a triangle]

                                3a     = 180

                              3a/3   = 180 / 3          [divide on both sides with 3 to get "a" alone]

                                   a     = 60

Each of the angles will be equal to 60 degrees.

Emphasize that:

• Learners should try to put the equal (=) sign underneath each other.
• Whatever you do on the left hand side of the equation, you also have to do on the right hand side.  
• Drawings are not always drawn to scale. (A protractor is not used to measure these angles)
• Angles are calculated by doing calculations.