Understanding Arcs and Circles

The video tutorial covers the concept of arc measures in geometry, starting with central angles and their role in defining arcs. It explains the differences between minor, major arcs, and semicircles. The tutorial also demonstrates how to measure arcs using central angles and provides a practical example using a pie chart to calculate arc measures based on percentages. Finally, it discusses congruent circles and arcs, explaining how to determine if they are congruent based on their measures and radii.

What is a central angle?

• An angle with its vertex at the center of a circle

• An angle that is formed by two radii

• An angle that is half of a circle

• An angle that measures 90 degrees

How is a major arc different from a minor arc?

• A major arc is less than half of the circle

• A major arc is more than half of the circle

• A major arc is exactly half of the circle

• A major arc is the same as a minor arc

What is the measure of an arc if the central angle is 70 degrees?

• 70 degrees

• 140 degrees

• 360 degrees

• 35 degrees

What is the relationship between the measure of a central angle and its arc?

• The arc is twice the central angle

• The arc is half the central angle

• The arc has the same measure as the central angle

• The arc is unrelated to the central angle

How do you calculate the measure of an arc in a pie chart if 48% of students use iPhones?

• 172.8 degrees

• 360 degrees

• 48% of 100 degrees

• 48 degrees

What is a semicircle?

• An arc that is more than half of the circle

• An arc that is less than half of the circle

• An arc that is exactly half of the circle

• An arc that is a quarter of the circle

What defines congruent circles?

• They have the same radius

• They have different diameters

• They have the same color

• They are drawn on the same paper

What is the most common way to determine the size of a circle?

• By its circumference

• By its radius

• By its color

• By its area

Which of the following is true about congruent arcs?

• They have different measures in congruent circles

• They have the same measure in congruent circles

• They are always semicircles

• They are always major arcs

If two arcs have the same measure but different radii, are they congruent?

• No, because they are different colors

• Yes, because they are in the same circle

• No, because they have different radii

• Yes, because they have the same measure