Download 11.4 Inscribed Angles: angles whose vertex is ON the circle and

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
page
8
page
9
page
10
Document related concepts
no text concepts found
Transcript 
May 11, 2012
11.4 Inscribed Angles: angles whose vertex is ON the
circle and whose sides contain
chords of the circle.
A
B
C
intercepted arc: arc on the interior of an inscribed
angle
May 11, 2012
Thm: The measure of an inscribed angle is equal
to one-half the measure of the intercepted
arc.
Examples.
1. Find mADC
2. Find mAC
B
A
B
C
A
70
C
May 11, 2012
Thm:
1. If a right triangle is inscribed in a circle, then the
hypotenuse is a diameter of a circle.
May 11, 2012
diameter
If one side of an inscribed triangle is a diameter,
then the triangle is right and the angle opposite
the diameter is right.
May 11, 2012
4. Find m A and m B
3. Find m B
B
A
80
C
196
A
B
May 11, 2012
Thm: If 2 inscribed angles intercept the same arc, then
angles are congruent.
5. Find m A, m B, and m C.
E
A
D
B
C
May 11, 2012
Defn.
inscribed polygon: all vertices are on the circle
circumscribed circle: circle around a polygon
touching all vertices of polygon.
May 11, 2012
A quadrilateral can be inscribed in a circle if and only
if the opposite angles are supplementary.
May 11, 2012
Find x.
6.
7.
x
3x
y
80
85
May 11, 2012
8.
19y
10y
40x
22x
Related documents