Draw three triangles on the board: one scalene, one isosceles and one equilateral triangle. Explain the difference between these types of triangles: scalene triangles have no equal sides or angles, isosceles triangles have two equal sides and angles and equilaterals have all three angles and sides equal. Ask students to use their rules -- so that they can measure the sides' length -- and construct a triangle of each type.
Explain to students that the sum of a triangle's angles can be no more and no less that 180 degrees. Help them understand that an alternative is impossible, by challenging them to prove this law wrong.
Design a right triangle on the board and tell students that it is called this way because it features a 90 degrees -- or right -- angle. Show students that a right angle is denoted with a square, instead of an arch. Name the corners using the letters C (for the right angle), D and E.
Tell students that the side opposite of the right angle is called the hypotenuse and denoted as "h." Afterwards, design three squares, using each side of the triangle as a square's side. Explain that the hypotenuse squares' area equals the sum of the other two squares' areas. This is the Pythagorean theorem, one of the most important trigonometric laws.
Write the Pythagorean theorem equation on the side of the board and erase the squares, leaving only the right triangle on the board. Explain to children that it is possible to calculate an unknown angle or side of a right triangle by using the trigonometric functions. The basic trigonometric functions are the sine, the cosine and the tangent.
Explain that the sine of an angle is the length of the opposite side side -- denoted "o" --divided by the length of the hypotenuse. Cosine of an angle is the adjacent side -- denoted "a" -- divided by h, while tangent is o divided by a. Every angle between 0 and 90 degrees has its own distinct sine, cosine and tangent that students can find in the relevant trigonometric tables.
Write the informal term SOHCAHTOA on the board and explain how children can use it as a mnemonic to remember the three basic trigonometric functions. SOH stands for "Sine Opposite (divided by) Hypotenuse", CAH is "Cosine Adjacent (divided by) Hypotenuse" and TOA means "Tangent Opposite (divided by) Adjacent."