Examples of Major, Minor, and Semicircle Arcs

📚 Understanding Arcs: A Quick Study Guide

• 📏 Arc Definition: An arc is a portion of the circumference of a circle.
• ✨ Minor Arc: An arc that measures less than 180 degrees. It's named using its two endpoints (e.g., $\stackrel{\frown}{AB}$).
• 🌟 Major Arc: An arc that measures greater than 180 degrees but less than 360 degrees. It's named using its two endpoints and a point on the arc (e.g., $\stackrel{\frown}{ACB}$).
• 💫 Semicircle Arc: An arc that measures exactly 180 degrees. Its endpoints are the endpoints of a diameter. Named using its two endpoints and a point on the arc (e.g., $\stackrel{\frown}{ADB}$).
• 📐 Arc Measure: The measure of an arc is equal to the measure of its central angle.
• ➕ Arc Addition Postulate: The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs: $m\stackrel{\frown}{ABC} = m\stackrel{\frown}{AB} + m\stackrel{\frown}{BC}$.

Practice Quiz

1. Question 1: Which of the following is true about a minor arc?
   1. A) It measures more than 180 degrees.
   2. B) It measures exactly 180 degrees.
   3. C) It measures less than 180 degrees.
   4. D) It measures 360 degrees.
2. Question 2: What is the measure of a semicircle arc?
   1. A) 90 degrees
   2. B) 180 degrees
   3. C) 270 degrees
   4. D) 360 degrees
3. Question 3: How many points are used to name a major arc?
   1. A) One
   2. B) Two
   3. C) Three
   4. D) Four
4. Question 4: If $\stackrel{\frown}{AB}$ measures 60 degrees, and $\stackrel{\frown}{BC}$ measures 40 degrees, what is the measure of $\stackrel{\frown}{ABC}$?
   1. A) 20 degrees
   2. B) 60 degrees
   3. C) 80 degrees
   4. D) 100 degrees
5. Question 5: Which of the following is NOT true about arcs?
   1. A) A minor arc is less than a semicircle.
   2. B) A major arc is greater than a semicircle but less than the entire circle.
   3. C) A semicircle is half of a circle.
   4. D) A major arc is always less than 180 degrees.
6. Question 6: A central angle of a circle measures 110 degrees. What is the measure of its corresponding minor arc?
   1. A) 55 degrees
   2. B) 70 degrees
   3. C) 110 degrees
   4. D) 220 degrees
7. Question 7: What is the difference between a major arc and a minor arc?
   1. A) A major arc is shorter than a minor arc.
   2. B) A major arc is longer than a minor arc.
   3. C) A major arc is equal in length to a minor arc.
   4. D) There is no difference.