10.1-10.4 Theorems

Theorem 10.1 - Tangent Line to a Circle Theorem

A line is Tangent to a circle if and only if a line is perpendicular to a radius of the circle at its endpoint on the circle.

Theorem 10.2 - External Tangent Congruence Theorem

Tangent segments from a common external point are congruent.

Postulate 10.1 - Arc Addition Postulate

The measure of an arc formed by 2 adjacent arcs is the sum of the measure of the 2 arcs.

Theorem 10.3 - Congruent Circles Theorem

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

Theorem 10.4 - Congruent Central Angles Theorem

In the same circle of congruent circles 2minor arcs are congruent if and only if their corresponding central angles are congruent.

Theorem 10.5 - Similar Circles Theorem

All circles are the same

Theorem 10.6 - Congruent Corresponding Chords

In the same circle or in congruent circles 2 minor arcs are congruent if and only if their corresponding chords are congruent.

Theorem 10.7 - Perpendicular Chord Bisector Theorem

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

Theorem 10.8 - Perpendicular Chord Bisector Converse

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

Theorem 10.9 - Equidistant Chords Theorem

In the same circle or in congruent circles 2 chords are congruent if and only if they are equidistant from the center.

Theorem 10.10 - Measure of an Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

Theorem 10.11 - Inscribed Angles of a Circle Theorem

If 2 inscribed angles of a circle intercept the same arc then the angles are congruent.

Theorem 10.12 - Inscribed Right Triangle Theorem

If the right triangle is inscribed in a circle then the hypotenuse is a diameter of the circle. Conversely if one side of an inscribed triangle is a diameter of the circle then the triangle is a right triangle and the angle opposite the diameter is the right angle.

Theorem 10.13 - Inscribed Quadrilateral Theorem

A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.