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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Quiz

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Exercise 16 Page 552

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? No.
Explanation: See solution.

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.

The angles of the circles have the same measure and, therefore, are congruent. However, the radii do not have the same length, which means that the circles are not congruent. Therefore, according to the theorem the red arcs are not congruent.