Download Lap 6 Definitions and Conjectures Congruent Circles: Two or more

Lap 6 Definitions and Conjectures
Congruent Circles: Two or more circles with congruent radii.
Concentric Circles: Two or more circles sharing the same center.
Radius: A segment with one endpoint the center of the circle and the other one on the circle.
Chord: A segment with endpoints on the circle (The diameter IS a chord).
Diameter: A chord that passes through the center of the circle.
Tangent: A line or segment that touches a circle (curve) at one point.
Semicircle: An arc with length half of the circumference of a circle or just half of a circle.
Minor arc: An arc shorter than semicircle. Major arc: An arc longer than semicircle (use 3
letters to notate it). Central Angle: Angle with its vertex at the center of the circle.
Inscribed Angle: Angle with its vertex on the circle (the sides of the angles are chords).
Chord Central Angles Conjecture C-54: If two chords in a circle are congruent, then they
determine two congruent central angles.
Chord Arcs Conjecture C-55: If two chords in a circle are congruent, then their intercepted arcs
are congruent.
Perpendicular to a Chord Conjecture C-56: The perpendicular from the center of a circle to a
chord is the bisector of the chord.
Chord Distance to Center Conjecture C-57: Two congruent chords in a circle are equidistant
from the center of the circle.
Perpendicular Bisector of a Chord Conjecture C-58: The perpendicular bisector of a chord
passes through the center of the circle.
Tangent Conjecture C-59: A tangent to a circle is perpendicular to the radius drawn to the point
of tangency.
Tangent Segments Conjecture C-60: Tangent segments to a circle from a point outside the
circle are congruent.
Inscribed Angle Conjecture C-61: The measure of an angle inscribed in a circle is half of the
measure of the central angle.
Inscribed Angles Intercepting Arcs Conjecture C-62: Inscribed angles that intercept the same
arc are congruent.
Angles Inscribed in a Semicircle Conjecture C-63: Angles inscribed in a semicircle are right
angles.
Cyclic Quadrilateral Conjecture C-64: The opposite angles of a cyclic quadrilateral are
supplementary.
Parallel Lines Intercepted Arcs Conjecture C-65: Parallel lines intercept congruent arcs on a
circle.
Circumference Conjecture C-66: The circumference of a circle is given by the formula C=πd or
C=2πr. Arc Length Conjecture C-67: The length of an arc equals the circumference times the
measure of the central angle divided by 360.