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Presentation transcript:

Warm – up

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

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?

Diameters are our friends

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

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

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

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

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

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

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

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

http://www.geogebra.org/en/upload/files/english/Guy/Circles_and_angles/Inscribed_Quadrilateral.html

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

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

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

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

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