Download Warm-Up Exercises

Warm-Up
Exercises
Bell Work
1. The measure of the interior angles of a quadrilateral
are 80º, 100º, 55º, and 5xº. Find the value of x.
2. Two supplementary angles have measures 6xº and
12xº. Find each angle measure.
1
3. Solve 3x = ( 4x + 12).
2
Warm-Up
Exercises
Notes
Definitions
An inscribed angle is an angle whose vertex is on a
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 intercepted arc
of the angle.
Warm-Up
Exercises
Notes
Theorem 10.7
Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is one half the
measure of its intercepted arc.
Warm-Up1Exercises
EXAMPLE
Find the indicated measure in
a.
m
T
b.
mQR
P.
Warm-Up2Exercises
EXAMPLE
Find mRS and m
and RUS?
STR. What do you notice about
STR
Warm-Up
Exercises
Notes
Theorem 10.8
If two inscribed angles of a circle intercept the same arc,
then the angles are congruent.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the measure of the red arc or angle.
1.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the measure of the red arc or angle.
2.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the measure of the red arc or angle.
3.
Warm-Up
Exercises
Notes
Definitions
A polygon is an inscribed polygon if all of its vertices
lie on the circle.
The circle that contains the vertices is a circumscribed
circle.
Warm-Up
Exercises
Notes
Theorem 10.9
If a right triangle is inscribed in a circle, then the
hypotenuse is a diameter of the circle.
Conversely, if one side of an inscribed triangle is a
diameter of the circle, then the triangle is a right triangle
and the angle opposite the diameter is the right angle.
Warm-Up4Exercises
EXAMPLE
Your camera has a 90o field of vision and you want to
photograph the front of a statue. You move to a spot
where the statue is the only thing captured in your
picture, as shown. You want to change your position.
Where else can you stand so that the statue is
perfectly framed in this way?
Warm-Up4Exercises
EXAMPLE
SOLUTION
From Theorem 10.9, you know that if a right triangle is
inscribed in a circle, then the hypotenuse of the
triangle is a diameter of the circle. So, draw the circle
that has the front of the statue as a diameter. The
statue fits perfectly within your camera’s 90o field of
vision from any point on the semicircle in front of the
statue.
Warm-Up
Exercises
GUIDED
PRACTICE
4. What If ? In Example 4, explain how to find locations
if you want to frame the front and left side of the
statue in your picture.
SOLUTION
Make the diameter of your circle the diagonal of the
rectangular base.
Warm-Up
Exercises
Notes
Theorem 10.10
A quadrilateral can be inscribed in a circle if and only if
its opposite angles are supplementary.
(not all quadrilaterals can be inscribed in a circle)
Warm-Up5Exercises
EXAMPLE
Find the value of each variable.
a.
Warm-Up
Exercises
GUIDED
PRACTICE
Find the value of each variable.
6.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Find the value of x .
1.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Find the value of x .
2.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Find the value of x .
3.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Find the value of each variable.
4.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Find the value of each variable.
5.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 10.4 (pg. 666-667) #2,8,12,14,17,20-25