Measuring Arcs and Central Angles. Measuring Arcs Arcs can be measured in two ways, by their length, or by degree For now, we will be measuring arcs only.

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ARCS AND CENTRAL ANGLES

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Presentation transcript:

Measuring Arcs and Central Angles

Measuring Arcs Arcs can be measured in two ways, by their length, or by degree For now, we will be measuring arcs only by degree.

Consider a whole circle In a whole circle, there are 360 degrees. A half circle, the arc between the end points of the diameter, measures 180 ̊.

Now, think about this…. If I cut the circle in half again, the new arc is 90 ̊. And the angle formed by the perpendicular diameters is a right angle … 90 ̊

Which Brings Us To……… THE CENTRAL ANGLE THEOREM! Remember: a CENTRAL ANGLE is an angle whose vertex is the center of the circle.

Central Angle Theorem The arc captured by the rays of a central angle has the same degree as that angle. 90 ̊

Central Angle Theorem The arc captured by the rays of a central angle has the same degree as that angle. 62 ̊ 120 ̊ 175 ̊

Assignment Pages #20-38 skip #35