University:
High School
Course:
High School Geometry
Academic year:

2021
Views:

37

Pages:

30
Author:

Mia Li

Unit 10 Arcs and Angles of Circles ) Lesson 1: Circles, Diameters and Radii Lesson 2: Central Angles and Arcs Lesson 3: Inscribed Angles and Arcs Lesson 4: Proving Circles Similar and Measures of Arcs Lesson 5: Circles, Chords, Diameters and their Relationships Angle Graded Practice Lesson 6: Arcs and Chords Quiz Lesson 7: Arc Length and Areas of Sectors Lesson 8: Unknown Length and Area ProЫems Test Review Test - Part 11, 111, IV Test- Partl - ' - _./ Practice: In circle О, АС is the diameter, mLCOD = 120° , and BD Ьisects LADO. ) Find the following. (10 а. mLAOD ь. mLOAD GO с. mLBDA 30 в Со d. mLBEC �:) е. mLACD · 30 f mLAВD ) D �о Summary h 1· -Р.____ the measure of the central • The inscribed angle is -�-" ' n...._., angle. • The central angle is the measure ofthe inscribed angle. -fwiC� 10-8 Unknown Length and Area ProЫems J Opening Exercise: 1. Find the exact area of the shaded region. А: ,7гг ;;._ --7rГ с: 2. ( ) ).. 7Г(q ) -;.- '7Т(:7 5) ·2. Find the area ofthe shaded region to the nearest tenth. Example 1: Another way to measure angles: (т V \ ·, ,,С}\ '··,_\':'::\,,\ С9 v-.-pc: .5'_� Draw c1rcle А of any size. 1. -) Draw in radius АВ. 2. Measure the radius using your compass. 3. 4. Using your compass at the same distance, measure and mark the number times needed to go around the circle once. ., s А 1 Approximately how many compass marks did it take to make it all the way around the circle? Was ) __ this the same for everyone in the class? . \.'�~\;) - J ,,v-ег lo ,, 'с,>1 -l ме \ -1-tпе I гоd, (.; ( I г )\ G (� С::Gг Using the approximation of 3.14 for п:, what is the relationship between the circumference and radius? С;:Gг С:: :;r;1-г .:::: ,;2(3. !Ч)r ;;с;, C,Pi,- The central angle that intercepts two consecutive compass markings оп your arc is equal to 1 radian. ) Diagram Definition -- ,......... ...., Radian • the measure of а central angle when the arc it subtends is equal in length to the radius (' .I� 1 ' \, , 1 �/ ... ....... __...... , In Example 1, we saw that it takes 2л: radii to go all the way around any circle. (С= 2л:r) Therefore, 2л: radians = 360 ° . How can we determine the number of degrees there are in 1 radian? - /! }r-.....,, -· -1 ) 5�.v • 1 I )( Formulas (оп Reference Sheet!) Radians ) Degrees 1 rad.1an = 180 degrees 1 degree = _!!__ radians 180 Example2: Circle В has а radius of 10 cm. and the measure of central angle В is 1.5 radians. Find the length ofthe intercepted arc. 1fo_ / .: с;т ) :: Example 3: prcle В has а radius of 14 cm. Angle В intercepts the arc with а length of бл:. Find the measure of angle В in radians.