body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

2. Finding Arc Measures

Continue to next subchapter

Exercise 21 Page 543

In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.

Are the Arcs Congruent? Yes.
Explanation: The circles are congruent and mVW=mXY.

Practice makes perfect

Before we determine whether the minor arcs are congruent, let's recall the Congruent Central Angles Theorem.

Congruent Central Angles Theorem
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent.

With this in mind, let's consider the given diagram.

We can see that the diameter of the circle on the right is 16, so its radius is 8. Since the radii have the same length, the circles are congruent. Also, the angles have the same measure, which means that they are congruent. Therefore, according to the theorem the red arcs are congruent.

Subchapter links

Communicate Your Answer p.537

Monitoring Progress p.539-541