theorems page 4 Flashcards
law of cosines
A squared equals B squared plus B squared -2 BC cosineA
tangent line to circle
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 it’s end point on the circle
external tangent congruence theorem
tangent segments from a common external point are congruent
congruent circles theorem
two circles are congruent circles if and only if they have the same radius
congruent central angles theorem
in the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent
similar circles theorem
all circles are similar
congruent corresponding chords theorem
in the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent
perpendicular cord by sector theorem
if a diameter of a circle is perpendicular to a chord then the diameter bisects the cord and it’s arc
perpendicular cord bisector converse
if one cord of a circle is a perpendicular bisector of another cord then the first cord is a diameter
equidistant cord theorem
in the same circle, or in congruent circles, two cords are congruent if and only if they are equidistant from the center
Measure of an inscribed angle theorem
The measure of an inscribed angle is one half the measure of its intercepted arc
inscribed angles of a circle theorem
if two inscribed angles of a circle intercept the same arc then the angles are congruent
inscribed right triangle theorem
if a right triangle is inscribed in a circle then the hypotenuse is a diameter of the circle
inscribed quadrilateral theorem
A quadrilateral can be inscribed in a circle if and only if it’s opposite angles are supplementary
tangent and intersected cord theorem
if a tangent and a cord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc
