Geometry Test #9 Flashcards
Center
A point that’s equidistant from any point on a circle.
Radius
A line segment that runs from a circle’s center to a point on the given circle.
Diameter
A chord that runs through a circle’s center.
Chord
A segment that connects any two points on a given circle.
Central Angle
An angle whose vertex is a given circle’s center and whose legs or sides intersect the circle.
Inscribed Angle
An angle whose vertex lies on a given circle and whose legs or sides intersect the circle at two other points.
Secant
A line, ray, or segment that intersects a given circle at more than one point.
Tangent
A line, ray, or segment that intersects a given circle at only one point (even if extended).
The angle between… is always right.
The angle between a tangent and a radius to the point of tangency is always right.
Segments… are congruent.
Segments tangent to the same circle drawn from the same point are congruent.
Radii….
Radii of the same circle are congruent.
If two chords are congruent…
If two chords are congruent, their intercepted arcs are congruent.
An inscribed angle measures….
An inscribed angle measures half its intercepted arc.
An angle formed by a tangent and chord measures…
An angle formed by a tangent and chord measures half the chord’s intercepted arc.
What angle measures 90 degrees?
An angle inscribed in a semicircle measures 90 degrees.
What angles of a quadrilateral are supplementary?
Opposite angles of quadrilaterals are supplementary.
Relationship between a central angle and an inscribed angle?
Measure of a Central Angle is twice the measure of any Inscribed Angle that intercepts the same arc.
Intersection of chords
part * part = part * part
A tangent to a circle
A tangent to a circle is perpendicular to the radius (or diameter) drawn at the point of tangency.
In the same circle or congruent circles, 2 arcs are
In the same circle or congruent circles two arcs are congruent if and only if their central angles are congruent.
In the same circle or congruent circles,
a) congruent arcs have…
In the same circle or congruent circles,
a) congruent arcs have congruent chords
b) congruent chords have congruent arcs
If the radius (diameter) is perpendicular…
If the radius (diameter) is perpendicular to a chord, than it bisects the chord and its corresponding arcs.
In the same circle or congruent circles
a) the chords that are
In the same circle or congruent circles
a) the chords that are equidistant from the center(s) are congruent
b) congruent chords are equidistant from the center(s)
Inscribed Angle Thm
The measure of an inscribed angle is equal to 1/2 the measure of its intercepted arc.
If two inscribed angles intercept…
If two inscribed angles intercept the same arc, then the angles are congruent.
Inscribed in a semicircle
An angle inscribed in a semicircle, is a right angle.
Angles in a quadrilateral
Opposite angles of a quadrilateral inscribed in a circle are supplementary.
The measure of an angle formed by a chord and a tangent…
The measure of an angle formed by a chord and a tangent is equal to 1/2 the measure of its intercepted arc.
Parallel Chords
Parallel chords create congruent arcs between them.
m<1=1/2(k+j)
The measure of an angle formed by two chords that intersect inside a circle is equal to 1/2 the sum of the measure of the intercepted arcs.
ab=cd
When two chords intersect inside a circle, the product of the segments equals the product of the segments of the other chord.
m<P=1/2(k-j)
(tangents)
The measure of an angle formed by two tangents drawn from a point outside a circle is equal to half the difference of the measure of the intercepted arcs.
t=q
(congruent tangents)
Tangents from an external point to a circle are congruent.
m<P=1/2(k-j)
(secants)
The measure of an angle formed by two secants drawn from a point outside a circle is equal to half the difference of the measure of the intercepted arcs.
(whole)(outer)=(whole)(outer)
secant segments
When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment is equal to the product of the other secant segment and its external segment.
m<P=1/2(k-j)
The measure of an angle formed by a secant and a tangent drawn from a point outside the circle is equal to half the difference of the measure of the intercepted arcs.
