Inscribed Angles and Cyclic Quadrilaterals

Vocabulary flashcards covering inscribed angles, intercepted arcs, cyclic quadrilaterals, and related geometric theorems and corollaries.

Inscribed Angle

An angle whose sides contain the endpoints of an arc of a circle and whose vertex is a point of the circle different from these endpoints.

Intercepted Arc

The arc whose points are either on an inscribed angle or in its interior.

Theorem 1.2 (Inscribed Angle Theorem)

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

Corollary 1 (Congruent Inscribed Angles)

Two inscribed angles that intercept the same arc or congruent arcs are congruent.

Corollary 2 (Inscribed Angle Intercepting a Semi-Circle)

An inscribed angle that intercepts a semi-circle is a right angle.

Corollary 3 (Opposite Angles of a Cyclic Quadrilateral)

Opposite angles of a cyclic quadrilateral are supplementary.

Corollary 4 (Exterior Angle of a Cyclic Quadrilateral)

Each exterior angle of a cyclic quadrilateral is congruent to the opposite interior angle.

Theorem 1.3 (Converse of Cyclic Quadrilateral Theorem)

If opposite angles in a quadrilateral are supplementary, then the quadrilateral is cyclic.