Geometry Chapter 10 Proofs

Tangent Line to Circle theorem

A line is tangent to a circle if and only if it’s perpendicular to the radius.

External Tangent Congruence theorem

Tangent segments from the same point are congruent

Arc addition postulate

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

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

Converse of Perpendicular Chord bisector theorem

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 each other.

Inscribed Angles of a Circle theorem

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

Inscribed Right Triangle theorem

If a right triangle is inscribed in a circle, then the hypotenuse is the diameter

Inscribed Quadrilateral Theorem

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

Vertex ON theorem

If the vertex of an angle is ON the circle, then the angle measures a half of the intercepted arc