standard_description: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
problem_activity: Problem 1
Bisect the following angle using constructions. Write your steps for construction.
$${\overline{CA}\cong \overline{AB}}$$
[IMG]
Problem 2
You and your partner will be provided with a list of steps (in random order) needed to copy an angle using a compass and straightedge. Your task is to place the steps in the correct order, then follow the steps to copy the angle below.
[IMG]
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:50%"}, "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}], "_values": ["Draw circle", ": center", ", any radius."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$A$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$C$$"}], "_values": ["Label the intersections of circle", "with the sides of the angle as", "and"], "em": [{"_value": "."}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$B$$"}], "_values": ["Label the vertex of the original angle as", "."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${\\overrightarrow{ED}}$$"}], "_values": ["Draw", "."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${\\overrightarrow{EG}}$$"}], "_values": ["Draw", "as one side of the angle to be drawn."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$FA$$"}], "_values": ["Draw circle", ": center", ", radius", "."]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$EA$$"}], "_values": ["Draw circle", ": center", ", radius", "."]}]}, {"td": [{"em": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}]}], "_values": ["Label intersection of circle", "with", "as", "."], "span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$${\\overrightarrow{EG}}$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math-tex"]}, "_value": "$$E$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$F$$"}, {"_attributes": {"class": ["math-tex"]}, "_value": "$$D$$"}], "_values": ["Label either intersection of circle", "and circle", "as", "."]}]}]}]}]}


aligns: no