1. Warm – up

2. EOCT Practice Shift the Parabola up 5 units left 8 units
stretch it 2 units. c
Write the equation
In vertex form

3. Math II Day 29 (9-15-10) Standard MM2G3.b
Understand and use properties of central, inscribed, and related angles.
Today’s Question:
What are the other special relationships between chords and angles?

4. Diameters are our friends

5. What is the measure of angle x and angle y?
160 x y

6. 40  112  Examples 3. If m JK = 80, find m <JMK.
4. If m <MKS = 56, find m MS.
112  M Q K S J

7. If two inscribed angles intercept the same arc, then they are congruent.
72

8. m<A = m<B 5x = 2x+9 x = 3 In J, m<A= 5x and m<B = 2x + 9.
Example 5
In J, m<A= 5x and m<B = 2x + 9.
Find the value of x. A Q D J T U B
m<A = m<B
5x = 2x+9
x = 3

9. and stuff you have figured out already
New Stuff
and stuff you have figured out already

15. Classwork:
Page 201 #1 – 6
You have 15 minutes

16. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

17. A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

19. y = 70 z = 95 110 + y =180 z + 85 = 180 Example 8 Find y and z. z 110

20. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
180
diameter

21. x = 26 4x – 14 = 180/2 4x – 14 = 90 Example 6 H K N G
In K, GH is a diameter and m<GNH = 4x – 14. Find the value of x.
4x – 14 = 180/2 H K
4x – 14 = 90 N G
x = 26

22. x = 11 6x – 5 + 3x – 4 = 180/2 6x – 5 + 3x – 4 = 90 H K N G Example 7
In K, m<1 = 6x – 5 and m<2 = 3x – 4. Find the value of x.
6x – 5 + 3x – 4 = 180/2 H 2 K
6x – 5 + 3x – 4 = 90 1 N G
x = 11

23. Homework:
Page 208 #19 – 21
Page 209 #1-8,21,23