Geometry Unit 6 Conjectures

Tangent Conjecture

a tangent to a circle is perpendicular the radius is drawn to the point of tangency

Tangent Segment Conjecture

Tangent segments to a circle from a point outside the circle are congruent

Chords Arc Conjecture

If 2 chords in a circle are congruent then their intercepted arcs are congruent

Chord Central Angles Conjecture

If 2 chords in a circle are congruent, then they determine 2 central angles that are congruent

Perpendicular to a Chord Conjecture

the perpendicular from the center of a circle to a chord is the bisector of the chord

Perpendicular Bisector of a Chord Conjecture

The perpendicular bisector of a chord passes through the center of a circle

Chord distance to center conjecture

2 congruent chords in a circle are equidistant from the center of the circle

Inscribed Angle Conjecture

the measure of an angle inscribed in a circle is 1/2 the measure of the intercepted arc

Inscribed Angles Intercepting Arcs Conjecture

Inscribed angles that intercept the same arc are congruent

Angles Inscribed in a Semicircle Conjecture

Angles inscribed in a semicircle are right angles

Cyclic Quadrilateral Conjecture

The opposite angles of a cyclic quadrilateral are supplementary

Parallel Lines Intercepted Arcs Conjecture

Parallel lines intercept congruent arcs on a circle

Circumference Conjecture

If C is the circumference and D is the diameter of a circle, then there is a number π such that C\=dπ. If d\=2r where R is the radius, then C\=2πr

Arc Length Conjecture

The length of an arc equals the measure of the arc divided by 360 times the circumference