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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Review

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Exercise 18 Page 583

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: 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 radii have the same length. Therefore, 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

Exercises p.582-586