Interior Angle Measures in Polygons Theorem
The sum of the angle measures of an n-gon is given by the formula
S(n) = (n -2)180o
Exterior Angle Measures in Polygons Theorem
The sum of the exterior angle measures of an n-gon, one angle at each vertex, is 360o
iff all its sides r equal in measure & all its angles r = in measure
drawn inside the figure
drawn outside the figure
segments whose endpoints are on the circle
Perpendicular Bisector of a Chord Theorem
The perpendicular bisector of a chord of a circle passes through the center of the circle.
an angle w/ its vertex at the center of the circle
measure of an arc intercepted (cut off) by a central angle is = to the measure of that central angle
can be named w/ 2/3 letters (just remember that a major arc is named w/ 3 letters to distinguish it from a minor arc w/ the same endpts)
named with three letters
outside letters = diameter; Ex: arcSTU → SU is diameter
180 < arc < 360
named w/ 3 letters
an angle formed by two chords that intersect at a point ON a circle
the arc that lies within an inscribed angle
Inscribed Angle Measure Theorem
The measure of an inscribed angle of a circle is equal to half the measure of its intercepted arc.
Inscribed Right Angle Theorem
An inscribed angle whose intercepted arc is a semicircle is a right angle.
Equal Inscribed Angles Theorem
If 2 inscribed angles in the same circle intercept the same arc, then they are equal in measure.
Intersecting Chords Theorem
The measure of an angle formed by 2 chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.
.5 (a + b)
Secants & Tangents Theorem
The measure of an angle formed by 2 secants, 2 tangents, or a secant & a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.
.5 (big - small)
tips for finding angles
continue radius to diameter
use systems of equations
remember perpendicular rule