4. 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
5. 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
6. Theorems
10.6 - Inscribed Angle Theorem:
10.7 - Two Inscribed Angles:
10.8 - Inscribed Angles and Diameters:
Thursday, May 17, 2012
7. 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
8. 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
9. 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
10. Example 1
Find each measure.
a. m∠YXW
b. m XZ
Thursday, May 17, 2012
11. Example 1
Find each measure.
a. m∠YXW
1
m∠YXW = mYW
2
b. m XZ
Thursday, May 17, 2012
12. Example 1
Find each measure.
a. m∠YXW
1 1
m∠YXW = mYW = (86)
2 2
b. m XZ
Thursday, May 17, 2012
13. Example 1
Find each measure.
a. m∠YXW
1 1
m∠YXW = mYW = (86) = 43°
2 2
b. m XZ
Thursday, May 17, 2012
14. Example 1
Find each measure.
a. m∠YXW
1 1
m∠YXW = mYW = (86) = 43°
2 2
b. m XZ
m XZ = 2m∠XYZ
Thursday, May 17, 2012
15. Example 1
Find each measure.
a. m∠YXW
1 1
m∠YXW = mYW = (86) = 43°
2 2
b. m XZ
m XZ = 2m∠XYZ = 2(52)
Thursday, May 17, 2012
16. Example 1
Find each measure.
a. m∠YXW
1 1
m∠YXW = mYW = (86) = 43°
2 2
b. m XZ
m XZ = 2m∠XYZ = 2(52) =104°
Thursday, May 17, 2012
17. Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
Thursday, May 17, 2012
18. Example 2
Find m∠QRT when m∠QRT = (12x − 13)° and m∠QST = (9x + 2)°.
12x −13 = 9x + 2
Thursday, May 17, 2012
19. 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
20. 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
21. 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
22. 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
23. 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
24. Example 3
Prove the following.
Given: LO ≅ MN
Prove: MNP ≅LOP
Thursday, May 17, 2012
25. 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
26. Example 4
Find m∠B when m∠A = (x + 4)° and m∠B = (8x - 4)°.
Thursday, May 17, 2012
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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
34. 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
37. 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