Tracing Angles and Angles in Radians
Angle Transport Postulate*
Consider in a plane an angle AÔB and a ray O'A'. On this plane, and in the half-plane, which O'A' allows to determine, there is a single ray O'B' that forms with O'A an angle A'Ô'B'. This angle is congruent to the AÔB angle.
Dupplicating an angle
Dupplicating an angle is the same as constructing an angle with the same measure as the first.
- Select the COMPASS tool (Window 5). Then click on points O and B (represent the length opening of the compass) and O (represent the sharp end of the compass).
- Select the INTERSECT tool (Window 2) and mark point D, which is the intersection point between the circle and the ray OA.
- Select the COMPASS tool (Window 5). Then, click on the points O and B (they represent the length opening of the compass) and on O' that is in the other ray.
- Select the INTERSECT tool (Window 2) and mark point E, which is the intersection point between the circle and the ray OB.
- Select the COMPASS tool (Window 5). Then, click on the points B and D (they represent the length opening of the compass) and on E that is in the other ray.
- Select the INTERSECT tool (Window 2) and mark a point F, which is the intersection point between the last two circles. Right-click on point F and rename it to A'.
-Select the RAY tool (Window 3) and click on O' and A'.
- Select the SHOW/HIDE OBJECT tool (Window 7) and hide the circles and the points E and D.
- Select the ANGLE tool (Window 7). Click on B', O' and A' to draw the angle mark B'O'A' (the vertex of the angle will always be the second point clicked). What can you see?
- Select the MOVE (Window 1) and change the positions of points A, B and/or B'
Analysis
Write an explanation for the structure.
ANGLES IN RADIANS
Analysis 1
Change the position of point E. Do the radius and arc measurements change? What is the quotient of the division?
Analysis 2
Change the position of point A. Do the radius and arc measurements change? What is the quotient of the division? Are the two division quotients the same?
Analysis 3
Change the position of point A until the angle is 180º. What is the quotient of the division? Do you recognize that number?
Research
Search for a good angle definition in radians and write it here.