INSCRIBED ANGLES Ms. “G”

Ben Hill Griffin Stadium

What does it mean to be INSCRIBED?

What kind of line segment is CD??

C D A

How would you determine the measure of arc CD?

How would you draw your “viewing angle” from A to edges of field? Where would you sit??? A

What kind of angle is angle A?

will be exploring the properties of inscribed angles of circles! TODAY: will be exploring the properties of inscribed angles of circles!

TEAMWORK Use your ruler and dry erase markers to draw a central angle within the circle Use the protractor to measure the central angle and record in the chart below Use your ruler to draw the inscribed angle that opens up onto the same intercepted arc Use your protractor to measure the inscribed angle and record in the chart below Repeat steps 1-4 for 5 different central angles

Inscribed Angle Measure Intercepted Arc Measure (degrees) Central Angle Measure Inscribed Angle Measure Intercepted Arc Measure (degrees) Angle 1 Angle 2 Angle 3 Angle 4 Angle 5

What do you notice about the intercepted arc measure compared to its Inscribed Angle measure?

WRITE THIS DOWN AND STAR IT!!!  the measure of the inscribed angle equals ½ the measure of its intercepted arc

Draw the central angle that corresponds to the intercepted arc AC Use the diagram on the back of your worksheet to complete the following: Draw the central angle that corresponds to the intercepted arc AC Draw 3 new inscribed angles in the given circle using the same endpoints A and C that the original inscribed angle uses. Use a different color for each angle. Measure each inscribed angle in the circle, the central angle, & record the intercepted arc measure in chart

Inscribed Angle Measure Central Angle Measure Inscribed Angle Measure Intercepted Arc Measure (degrees) Angle 1 Angle 2 Angle 3 Angle 4

What is the measure of these new inscribed angles? WHY? What can you conclude about this discovery?

WRITE THIS DOWN AND STAR IT!!!  if two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent

Suppose your friend tells you that the best seat in the football stadium is near the 50 yard line, within the area enclosed by the circle inscribing the field: your seat is marked with letter S in the diagram. Draw your viewing angle with endpoints on the edges of circle’s diameter.

S

If this seat is taken what other seats can you choose along the circle to ensure you the SAME viewing angle of the field?

What are the measures of ALL of these inscribed angles?

If the endpoints of the angle terminated before the diameter, what is the viewing angle What about after?

What can we conclude from these observations? WRITE THIS DOWN AND STAR IT!!!  If an inscribed angle of a circle intercepts a diameter or a semicircle, then the inscribed angle is a RIGHT ANGLE!