Chapter10Theorems

Question 1

External tangent congruence theorem

Answer 1

Tangent segments from a common external point are congruent

Question 2

Tangent line to circle theorem

Answer 2

In a plane a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle

Question 3

Arc addition postulate

Answer 3

the measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs

Question 4

congruent circles theorem

Answer 4

two circles are congruent circles if and only if they have the same radius

Question 5

congruent central angles theorem

Answer 5

in the same circle or congruent circles two minor arcs are congruent if and only if their corresponding central angles are congruent

Question 6

similar circles theorem

Answer 6

all circles are similar

Question 7

congruent corresponding chords theorem

Answer 7

in the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent

Question 8

perpendicular chord bisector theorem

Answer 8

if a diameter of a circle is perpendicular to a chord then the diameter bisects the chord and its arc

Question 9

perpendicular chord bisector converse

Answer 9

if one chord of a circle is a perpendicular bisector of another chord then the first chord is a diameter

Question 10

equidistant chords theorem

Answer 10

in the same circle or in congruent circles two chords are congruent if and only if they are equidistant from the center

Question 11

measure of an inscribed angle theorem

Answer 11

the measure of an inscribed angle is one half the measure of its intercepted arc

Question 12

inscribed angles of a circle theorem

Answer 12

if two inscribed angles of a circle intercept the same arc then the angles are congruent

Question 13

inscribed right triangle theorem

Answer 13

inscribed angles with endpoints that are the same as the diameter are right angles

Question 14

inscribed quadrilateral theorem

Answer 14

a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary

Question 15

tangent and intersected chord theorem

Answer 15

if a tangent and a chord intersect at a point on a circle then the measure of each angle formed is one half the measure of its intercepted arc

Question 16

Angles inside the circle theorem

Answer 16

If two chords intersect inside a circle then the measure of each angle if one half the sum of the measures of the arcs intercepted by the angle and its vertical angle

Question 17

Angles outside the circle theorem

Answer 17

If a tangent and a secant, two tangents, or two decanted intersect outside a circle then the measure of the angle formed is one half the difference of the measures of the intercepted arcs

Question 18

Circumscribed angle theorem

Answer 18

The measure of a circumscribed angle is equal to 180 minus the measure of the central angle that intercepts the same arc

Question 19

Segments of chords theorem

Answer 19

If two chords intersect in the interior of a circle then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord

Question 20

Segments of secants theorem

Answer 20

If two secant segments share the same endpoint outside a circle then the product of the lengths of one secant segment and it’s external segment equals the product of the lengths of the other secant segment and it’s external segment

Question 21

Segments of secants and tangents theorem

Answer 21

If a secant segment and a tangent segment share an endpoint outside a circle then the product of the lengths of the secant segment and it’s external segment equals the square of the length of the tangent segment