Central Angles.

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Presentation transcript:

Central Angles

<APB is a Central Angle Central Angle : An Angle whose vertex is at the center of the circle A Major Arc Minor Arc More than 180° Less than 180° ACB P AB To name: use 3 letters C To name: use 2 letters B <APB is a Central Angle

Semicircle: An Arc that equals 180° To name: use 3 letters E D EDF P F EF is a diameter, so every diameter divides the circle in half, which divides it into arcs of 180°

THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs are Supplementary

Vertical Angles are Equal

Linear Pairs are Supplementary http://www.mathopenref.com/linearpair.html 120° 60°

measure of an arc = measure of central angle 96 Q m AB = 96° B C m ACB = 264° m AE = 84°

Arc Addition Postulate B m ABC = + m BC m AB

240 260 m DAB = m BCA = Tell me the measure of the following arcs. D 140 260 m BCA = R 40 100 80 C B

CONGRUENT ARCS Congruent Arcs have the same measure and MUST come from the same circle or from congruent circles. C B D 45 45 110 A

Classwork Page 193 #9-18 You have 15 minutes.

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… 160° 80°

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

What do we call this type of angle? What is the value of x? How do we solve for y? The measure of the inscribed angle is HALF the measure of the inscribed arc!! 120 x y

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

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

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

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

Classwork: Page 193 #9-23 Page 207 #1-15

Whatever is left is homework