Presentation on theme: "What’s Up for Today? LEARNING TARGET IN-CLASS HOMEWORK Geometry"— Presentation transcript:
1What’s Up for Today? LEARNING TARGET IN-CLASS HOMEWORK Geometry I can examine relationship between central and inscribe angles by applying theorems about their measure.I can solve the unknown measure of arcs and angles in a circle.Review on parts of circlePowerpoint presentation on circlesUse classwork notes to show answers for math problems.Sage and scribe activity(hand out)Exit slipsNo homework
2REVIEW Identify the following parts of the circle. A BEDCABACline EchordradiusdiametertangentsecantNote: The following are possible answers.radiusdiameterchordmidpointsecanttangent
4Types of Angles Central angle Inscribed angle - the vertex is on the center.Inscribed angle- the vertex is on the circle.
5Types of Arcs Major arc Minor arc Semicircle P M O N or MN - the measure is more than 180 °Example: MNOP- the measure is less than 180 °Example: MOO- the measure is equal to 180 °Nor MNExample: MON
6Solving Unknown Arcs and Angles On the next slides…you will use a white board (or a filler with printing paper), and a marker to solve and answer the given problems.you will be given 30 seconds to solve each of the math problems.at the end of each problem , you will raise your white board with your answer on it. Make sure you box your answer.Have fun!
7Measure of Arcs & Angles In a circle, the measure of the central angle is always equal to the measure of its intercepted arc.x = nm ∠ ABC = m ACn°CIf ∠ ABC is 80°, what is the measure of arc AC?Ax°B °m AC = 80°
8Measure of Arcs & Angles EXAMPLE: In the diagram below, if the m ∠ xyz is 68°, find the measure of a.) minor arc and b.) major arc.SOLUTION:a. measure of minor arcm ∠xyz = m xz (since ∠xyz is a central angle)xm xz = 68°b. measure of major arcmajor arc = 360° – m xz (minor arc)68°=360° – 68°m xz (major arc) = 292°68°y292°z
9Measure of Arcs & Angles The measure of inscribed angle is always equal to ½ the measure of its intercepted arc.x = ½ n or 2x = nm ∠ ABC = ½ (m AC)Cn°If ∠ ABC is 35°, what is the measure of arc AC?m AC = 70°Ax°B
10Measure of Arcs & Angles EXAMPLE: If the measure of the minor arc below is 68°, find the measure of the inscribe angle, ∠ ABC.SOLUTION:Inscribed angle = ½ (intercepted arc)∠ ABC = ½ (68°)∠ ABC= 34°AB34°68°C
11Examine the diagram and solve PROBLEM: If angle BAC is 24°, solve for xSOLUTION:Angle x is a central angle. Therefore, ∠ x = arc BC.Arc BC is an intercepted arc of inscribe angle ABC.Since inscribed angle = ½(intercepted arc),therefore, the intercepted arc is twice the inscribe angle. n = 2x∠ x = 2 (24)∠ x = 48°ADCentre of Circle24 °this is the arc BCxCB
12Examine the diagram and solve SOLVE: If m ∠PON is 105°, what is the measure of (a) arc PN?(b) m ∠ PMN?SOLUTION:Angle PON is a central angle.Therefore, ∠ PON = arc PMN.arc PMN = 105°a. Arc PN = ?= 360° – 105°Arc PN = 255°b. ∠ PMN = ?∠ PMN an inscribe angle and arc PN is its intercepted arc.Since inscribed angle = ½(intercepted arc),therefore,∠ PMN = ½ (255°)∠ PMN = 127.5°Centre of CircleMxNP105°OArc PN
13Sage and Scribe Activity Students will work in pairs.The first partner, the “sage”, will talk about the math problem, while the other student, the scribe will write it. If the sage is correct, the scribe praises the sage. Otherwise, the scribe coaches, then praises. Students swap roles for the next problem.Students will work for 4 minutes at voice level 1 (whisper).If you are done with 4 math problems, you are encourage to try the challenge problem at the bottom of hand out #3.Have fun!
14Remember…In a circle, the measure of the central angle is always equal to the measure of its intercepted arc. x = nThe measure of inscribed angle is always equal to ½ the measure of its intercepted arc.x = ½ n or 2x = n
15EXIT SLIP Use the diagram below to answer the following question: Find m BCFind the m BDCFind m ∠BACBD50°AC