Did you investigate the side length ratios in the two triangles? Would you categorize the side length ratios as being different or the same? Does changing the angle or scale factor of dilation change your obseration?
You are going to write an argument about why the side ratios in a right triangle are properties of the angles in the right triangle. In other words the side ratios depend upon the angle and DO NOT depend on the size of the triangle. This leads to the 6 definitions of the trigonometric ratios for acute angles in a right triangle.
The two triangle are __________________ because the two triangles have the _________________________.[br]Because the triangles are __________________, the side lengths are ______________________ which means there is a _____________________ that determines the side lengths of the similar triangle.[br]If you compare the ratio of two side of one triangle with corresponding ratio of sides in the other triangle, the ratios will be _______________ because _____________________________________________________________________.
Why can we define the sine, cosine, tangent, cotangent, secant, and cosecant of an angle [math]\theta[/math] regardless of the size of the triangle? How do we know that the trig ratio of an angle will always be the same number? For example, sin30 is constant (does not change). For example, cos72 is constant (does not change).