Download 11.5: Inscribed Angles and Polygons

Geometry
11.5: Inscribed Angles and Polygons
Name:____________________________
Review: Remember the relationship between central angles and their arcs:
An _________________ _________________ is an angle
whose vertex is on the circle and whose sides contain
chords of the circle.
The arc that lies in the interior of an inscribed angle
and has endpoints on the angle is called the
______________________ ____________.
Theorem:
If an angle is ________________________ in a circle, then its measure is
_______________ the measure of its intercepted arc.
Example 1: Find the measures below.
a. Find m∠NMP.
TRY:
a. Find m∠BCD.
̂.
b. Find m𝑍𝑊𝑋
̂
b. Find m𝐾𝑁𝑃
c. Find m∠DEF.
̂
c. Find m𝐾𝐿
Inscribed and Circumscribed
If all the vertices of a polygon lie on a circle, then the polygon is ________________ ___ the
circle and the circle is __________________________ ________________ the polygon.
If you inscribe a right triangle in a circle, then what is the
measure of the arc intercepted by the right angle?
What must be true about the hypotenuse of the triangle?
Theorem
1. If a triangle inscribed in a circle is a _______________________ ___________________,
then the hypotenuse is a ____________________ of the circle.
2. If a side of a triangle inscribed in a circle is a ________________,
then the triangle is a ________________ triangle.
Example 2: Find the values of x and y.
a)
b)
Theorem:
1. If a quadrilateral can be __________________ _____ a circle, then its
_________________ _________________ are ___________________________.
2. If the _______________________ ___________________ of a
quadrilateral are _______________________, then the
quadrilateral can be ________________ ____ a circle.
Example 3: Find the values of the variables.
a.
b.
TRY: Find the values of the variables.
a.
b.
c.
d.
Homework: p. 618 #9 – 19 odds, 21 – 26 all, 28 – 30, 32 - 34