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Section 10-4Inscribed Angles
Thursday, May 17, 2012
Essential Questions
How do you find measures of inscribed angles?
How do you find measures of angles on inscribed polygons?
Thursday, May 17, 2012
Vocabulary
1. Inscribed Angle:
2. Intercepted Arc:
Thursday, May 17, 2012
Vocabulary
1. Inscribed Angle: An angle made of two chords in a circle, so that the vertex is on the edge of the circle
2. Intercepted Arc:
Thursday, May 17, 2012
Vocabulary
1. Inscribed Angle: An angle made of two chords in a circle, so that the vertex is on the edge of the circle
2. Intercepted Arc: An arc with endpoints on the sides of an inscribed angle and in the interior of the inscribed angle
Thursday, May 17, 2012
Theorems
10.6 - Inscribed Angle Theorem:
10.7 - Two Inscribed Angles:
10.8 - Inscribed Angles and Diameters:
Thursday, May 17, 2012
Theorems
10.6 - Inscribed Angle Theorem: If an angle is inscribed in a circle, then the measure of the angle is one half the measure of the intercepted arc
10.7 - Two Inscribed Angles:
10.8 - Inscribed Angles and Diameters:
Thursday, May 17, 2012
Theorems
10.6 - Inscribed Angle Theorem: If an angle is inscribed in a circle, then the measure of the angle is one half the measure of the intercepted arc
10.7 - Two Inscribed Angles: If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent
10.8 - Inscribed Angles and Diameters:
Thursday, May 17, 2012
Theorems
10.6 - Inscribed Angle Theorem: If an angle is inscribed in a circle, then the measure of the angle is one half the measure of the intercepted arc
10.7 - Two Inscribed Angles: If two inscribed angles of a circle intercept the same arc or congruent arcs, then the angles are congruent
10.8 - Inscribed Angles and Diameters: An inscribed angle of a triangle intercepts a diameter or semicircle IFF the angle is a right angle
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
b. m XZ
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
m∠YXW =
12
mYW
b. m XZ
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
m∠YXW =
12
mYW =
12
(86)
b. m XZ
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
m∠YXW =
12
mYW =
12
(86) = 43°
b. m XZ
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
m∠YXW =
12
mYW =
12
(86) = 43°
b. m XZ
m XZ =2m∠XYZ
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
m∠YXW =
12
mYW =
12
(86) = 43°
b. m XZ
m XZ =2m∠XYZ =2(52)
Thursday, May 17, 2012
Example 1
Find each measure.
a. m∠YXW
m∠YXW =
12
mYW =
12
(86) = 43°
b. m XZ
m XZ =2m∠XYZ =2(52) =104°
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13=9x +2
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13=9x +2 3x =15
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13=9x +2 3x =15
x =5
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13=9x +2 3x =15
x =5
m∠QRT =12(5)−13
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13=9x +2 3x =15
x =5
m∠QRT =12(5)−13 =60−13
Thursday, May 17, 2012
Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13=9x +2 3x =15
x =5
m∠QRT =12(5)−13 =60−13 = 47°
Thursday, May 17, 2012
Example 3
Prove the following.
Given: LO ≅ MN
Prove: MNP ≅LOP
Thursday, May 17, 2012
Example 3
Prove the following.
Given: LO ≅ MN
Prove: MNP ≅LOP
There are many ways to prove this one. Work through a proof on your own. We will discuss a few in class.
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
9x +90=180
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
9x +90=180 9x =90
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
9x +90=180 9x =90 x =10
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
9x +90=180 9x =90 x =10
m∠B =8(10)−4
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
9x +90=180 9x =90 x =10
m∠B =8(10)−4 =80−4
Thursday, May 17, 2012
Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
m∠A+m∠B +m∠C =180 x +4+8x −4+90=180
9x +90=180 9x =90 x =10
m∠B =8(10)−4 =80−4 =76°
Thursday, May 17, 2012
Check Your Understanding
p. 713 #1-10
Thursday, May 17, 2012
Problem Set
Thursday, May 17, 2012
Problem Set
p. 713 #11-35 odd, 49, 55, 61
“You're alive. Do something. The directive in life, the moral imperative was so uncomplicated. It could be expressed in single words, not
complete sentences. It sounded like this: Look. Listen. Choose. Act.”- Barbara Hall
Thursday, May 17, 2012