Geometry Test #9 Flashcards

1
Q

Center

A

A point that’s equidistant from any point on a circle.

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2
Q

Radius

A

A line segment that runs from a circle’s center to a point on the given circle.

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3
Q

Diameter

A

A chord that runs through a circle’s center.

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4
Q

Chord

A

A segment that connects any two points on a given circle.

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5
Q

Central Angle

A

An angle whose vertex is a given circle’s center and whose legs or sides intersect the circle.

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6
Q

Inscribed Angle

A

An angle whose vertex lies on a given circle and whose legs or sides intersect the circle at two other points.

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7
Q

Secant

A

A line, ray, or segment that intersects a given circle at more than one point.

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8
Q

Tangent

A

A line, ray, or segment that intersects a given circle at only one point (even if extended).

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9
Q

The angle between… is always right.

A

The angle between a tangent and a radius to the point of tangency is always right.

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10
Q

Segments… are congruent.

A

Segments tangent to the same circle drawn from the same point are congruent.

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11
Q

Radii….

A

Radii of the same circle are congruent.

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12
Q

If two chords are congruent…

A

If two chords are congruent, their intercepted arcs are congruent.

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13
Q

An inscribed angle measures….

A

An inscribed angle measures half its intercepted arc.

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14
Q

An angle formed by a tangent and chord measures…

A

An angle formed by a tangent and chord measures half the chord’s intercepted arc.

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15
Q

What angle measures 90 degrees?

A

An angle inscribed in a semicircle measures 90 degrees.

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16
Q

What angles of a quadrilateral are supplementary?

A

Opposite angles of quadrilaterals are supplementary.

17
Q

Relationship between a central angle and an inscribed angle?

A

Measure of a Central Angle is twice the measure of any Inscribed Angle that intercepts the same arc.

18
Q

Intersection of chords

A

part * part = part * part

19
Q

A tangent to a circle

A

A tangent to a circle is perpendicular to the radius (or diameter) drawn at the point of tangency.

20
Q

In the same circle or congruent circles, 2 arcs are

A

In the same circle or congruent circles two arcs are congruent if and only if their central angles are congruent.

21
Q

In the same circle or congruent circles,
a) congruent arcs have…

A

In the same circle or congruent circles,
a) congruent arcs have congruent chords
b) congruent chords have congruent arcs

22
Q

If the radius (diameter) is perpendicular…

A

If the radius (diameter) is perpendicular to a chord, than it bisects the chord and its corresponding arcs.

23
Q

In the same circle or congruent circles
a) the chords that are

A

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)

24
Q

Inscribed Angle Thm

A

The measure of an inscribed angle is equal to 1/2 the measure of its intercepted arc.

25
If two inscribed angles intercept...
If two inscribed angles intercept the same arc, then the angles are congruent.
26
Inscribed in a semicircle
An angle inscribed in a semicircle, is a right angle.
27
Angles in a quadrilateral
Opposite angles of a quadrilateral inscribed in a circle are supplementary.
28
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.
29
Parallel Chords
Parallel chords create congruent arcs between them.
30
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.
31
a*b=c*d
When two chords intersect inside a circle, the product of the segments equals the product of the segments of the other chord.
32
m
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.
33
t=q (congruent tangents)
Tangents from an external point to a circle are congruent.
34
m
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.
35
(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.
36
m
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.