Download Geometry Section 10-4 - West End Public Schools

Geometry
Section 10-4
Use Inscribed Angles and
Polygons
Inscribed Angles
 An angle whose
vertex is on a circle
and whose sides
contain chords of the
circle
 Intercepted arc is the
arc that has the
endpoints on the
angle
Measure of an Inscribed Angle
 The measure of an
inscribed angle is one
half the measure of its
intercepted arc.
Congruent Inscribed Angles Theorem
 If two inscribed
angles of a circle
intercepts the same
arc, then the angles
are congruent
Inscribed Polygons
 All the vertices lie on
a circle
 The circle that
contains the vertices
is a circumscribed
circle
Inscribed Right Angle Theorem
 If a right angle is
inscribed in a circle, then
the hypotenuse is a
diameter of a circle.
 Also, if one side of an
inscribed angle is the
diameter, then the
triangle is a right triangle,
with the right angle
opposite the diameter
Inscribed Quadrilateral Theorem
 A quadrilateral can be
inscribed in a circle iff
its opposite angles
are supplementary
Examples
classzone.com
Assignment
Section 10-4
Page 676
Problems # 4-24 evens