On this day we will introduce
the folling special right triangles and do some student guided
examples.
A 45-45-90 triangle is an example of a special right triangle. An isosceles right triangle, which means it has two sides of equal length and a 90 angle, has two 45 angles and is called a 45-45-90 triangle. Since we know two sides of the triangle are equal then we also know that the angles opposite them are equal. You can find the length of the hypotenuse of a 45-45-90 triangle when the length of a leg is known.
45-45-90 Triangle Theorem
The length of the hypotenuse
of a 45-45-90 triangle is the square root of two times the length
of a leg.
A 30-60-90 triangle is another example of a special right triangle that has a 30 degree angle and a 60 degree angle. The hypotenuse and the longer leg in a 30-60-90 triangle can be found when the shorter leg is known. The shorter leg is opposite the 30 angle and the longer leg is opposite the 60 angle.
30-60-90 Triangle Theorem
In a 30-60-90 triangle, the length of the hypotenuse is 2 times the length of the shorter leg and the length of the longer leg is the square root of three times the length of the shorter leg.
After a few standard examples, the students will be given a worksheet to practice and hopefully commit to memory the theorems they learned.