Understanding Arcs and Central Angles

Mr. Greenstein's geometry class covers chapter 10, section 2 on finding arc measures. The lesson introduces central angles, minor and major arcs, and semicircles. Example problems demonstrate calculations involving diameters and isosceles triangles. The arc addition postulate is explained, followed by theorems on congruent circles and central angles. The session concludes with problems on congruent arcs and circles.

What is the main topic discussed in this session?

• Solving quadratic equations

• Finding arc measures

• Calculating area of circles

• Understanding parallel lines

What is a central angle?

• An angle that measures exactly 90 degrees

• An angle formed by two tangents

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

• An angle formed by two chords

Which of the following is true about a minor arc?

• It is always a semicircle

• It measures less than 180 degrees

• It is equal to the central angle

• It measures more than 180 degrees

How is a major arc defined?

• An arc that measures exactly 180 degrees

• An arc that measures less than 90 degrees

• An arc that measures more than 180 degrees

• An arc that is equal to the central angle

What is the measure of a semicircle?

• 360 degrees

• 90 degrees

• 270 degrees

• 180 degrees

What is the measure of a major arc?

• More than 180 degrees

• Exactly 180 degrees

• Exactly 90 degrees

• Less than 90 degrees

What is the measure of a minor arc?

• More than 180 degrees

• Exactly 180 degrees

• Less than 180 degrees

• Exactly 90 degrees

What is the measure of a semicircle?

• 270 degrees

• 360 degrees

• 180 degrees

• 90 degrees

If a central angle measures 59 degrees, what is the measure of the corresponding arc?

• 59 degrees

• 118 degrees

• 180 degrees

• 29.5 degrees

What is the relationship between the central angle and the arc in a circle?

• The central angle is always half the arc

• The central angle is unrelated to the arc

• The central angle is equal to the arc

• The central angle is twice the arc