Warm up Find the missing measures: 130° D A R 50 120° 60 C 230° B.

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Presentation transcript:

Warm up Find the missing measures: 130° D A R 50 120° 60 C 230° B

________ _____

Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INTERCEPTED ARC INSCRIBED ANGLE

Determine whether each angle is an inscribed angle Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 1. YES; CL C L O T

Determine whether each angle is an inscribed angle Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. NO; QVR 2. Q V K R S

To find the measure of an inscribed angle, divide the intercepted arc by 2… 160º 80º

To find the measure of an intercepted arc, multiply the inscribed angle by 2… 160º 80º

Ex. 1 Find m1. A B 1 124° C m1 = 62º

What do we call this type of angle? Inscribed Angle 60° What is the value of y? Central Angle What do we call this type of angle? 120 x y 120° What is the value of x?

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

If two inscribed angles intercept the same arc, then they are congruent. 72º A F B C

x = 3 5x = 2x+9 In J, m3 = 5x and m 4 = 2x + 9. Example: Find the value of x. 3 Q D J T U 4 5x = 2x+9 x = 3

If all the vertices of a polygon touch the edge of the circle, then 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

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

If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle AND the angle opposite the diameter is a right angle. 180º diameter

Example: In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G HINT: GH is also the __________ . Therefore, angle GNH is a ______ angle. hypotenuse right

Example 7 K is a right triangle. In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x. 6x – 5 + 3x – 4 = 90 H 2 K x = 11 1 N G HINT: Angle GNH is a ________ angle. Therefore, angles G & H are __________ . right complementary

Homework Pages 207-208 #s1-22