Download Inscribed-Angles-Notes-12.3

Geometry
Inscribed Angle Activity
Date: _________
In the next section, we are going to look at angles inscribed in circles. There are two kids of
angles that can be inscribed in a circle:
* An angle whose vertex is AT the center of the circle
* An angle whose vertex is ON the circle.
1. a)
AXB  _____
1  _____
2  _____
3  _____
m Arc AB  _____
2.
a)
4  _____
5  _____
6  _____
b) Conjecture:
b) Conjecture:
c) Conjecture:
In conclusion:
Geometry
Inscribed Angles Notes
Date: _____________
Objective 1: I can find the measure of an inscribed angle.
Let’s recap the activity: Below, the vertex of _____ is on ________, and the sides of ______
are _______ of the circle. ______ is an _________________. _____ is the
____________________ of _____.
Theorem 4 describes the relationship between an inscribed angle and its intercepted arc.
Theorem 4: Inscribed Angle Theorem
The measure of an inscribed angle is _________________________ of its intercepted arc.
There are three different ways that an angle can be inscribed inside of a circle.
I.
II.
III.
Regardless of where the center of the circle is located, you will still use Theorem 4 to find the
measure of inscribed angles.
Example 1: Use Theorem 4 to find the measure of inscribed angles.
A) Find the values of a and b.
B) Use the diagram above and find mPQR if m Arc RS = 60 .
C) Find the values of x and y in the circle below.
These corollaries below will help you find the measures of angles in circles.
Corollaries to the Inscribed Angle Theorem (theorem 4):
(1) Two inscribed angles that intercept
(2) An angle inscribed in a semicircle
the same arc are ________________.
is a ___________________.
Example 2: Use the above corollaries to find the measure of the numbered angles.
A)
B)
C) Find the values of a and b.
D) Find the value of x.