12.3 inscribed angles
DESCRIPTION
12.3 Inscribed Angles. Brett Solberg AHS ‘11-’12. Warm-up. 1) What is the measure of arc AC? 2) What is the arc length of arc AC? 3) Get out your notes and HW. HW Review. #8. Today’s Agenda. Quiz 12.3 Inscribed Angles Last day for retakes. Quiz. 3 Problems 6 minutes - PowerPoint PPT PresentationTRANSCRIPT
12.3 INSCRIBED ANGLESBrett Solberg AHS ‘11-’12
WARM-UP
1) What is the measure of arc AC?
2) What is the arc length of arc AC?
3)
Get out your notes and HW.
HW REVIEW
#8
TODAY’S AGENDA
Quiz 12.3 Inscribed Angles
Last day for retakes
QUIZ
3 Problems 6 minutes Use your notes Flip over when done
1) Is BC tangent to circle a? How do you know?
2) What is the perimeter of the polygon?
3) Find the value of x.
REVIEW
What is the difference between: arc length measure of an arc
Measure of an arc = measure of the central angle.
INSCRIBED CIRCLE
Inscribed Angle Angle whose vertex is on a circle and whose
sides are chords. Intercepted arc
Arc created by an inscribed angle.
EXAMPLE 1
Identify the inscribed angle and the intercepted arc.
THEOREM 12.9-INSCRIBED ANGLE THEOREM
The measure of an inscribed angle is half the measure of its intercepted arc.
ABC = ½AC
DEMONSTRATION
EXAMPLE 2
Find the measure of arc AC
EXAMPLE 2
Find the measure of arc PT and angle R.
EXAMPLE 2
Find the measure of angle G and angle D.
COROLLARIES TO THE INSCRIBED ANGLE THEOREM
1) Two inscribed angles that share an intercepted arc are congruent.
2) An angle inscribed by a semicircle is a right angle.
COROLLARIES TO THE INSCRIBED ANGLE THEOREM
3) The opposite angles of a quadrilateral inscribed in a circle are supplementary.
angle N + angle O = 180˚ angle P + angle M = 180˚
THEOREM 12.10
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
EXAMPLE 4
RS and TU are diameters of circle A. RB is tangent to circle A at point R. Find the measure of angle BRT and TRS.
ASSIGNMENT
Worksheet 2.3
EC Assignment Due on THU pg. 711 #1 – 43 all