Theorems and Postulates of Circles Chapter 10 Quiz 1-3

Tangent Line and Circle Theorem

In a plane, a line is tangent to a circle if and only if the line is perpendicular to the radius of the circle at its endpoint on the circle.

External Tangent Congruence Theorem

Tangent segments from a common external point are congruent.

Arc Addition Postulate

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Congruent Circles Theorem

Two circles are congruent circles if and only if they have the same radius.

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.

Similar Circles Theorem

All circles are similar.

Congruent Corresponding Chords Theorem

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

Perpendicular Chord Bisector Theorem

If a diameter to a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

Perpendicular Chord Bisector Converse

If one chord of a circle is a perpendicular bisector of another chord, then the first chord is a diameter.

Equidistant Chords Theorem

In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.