10.6 CIRCLES AND ARCSBrett Solberg AHS ‘11-’12
Today’s Schedule• 1st 7:55 – 9:35 am• ASSEMBLY 9:40 – 10:25 am Announcements 10:30
– 10:35 am• 2nd Period 10:35 – 11:35 am•
• 1st LUNCH 11:35 – 12:14 pm• 3RD PERIOD 12:20 – 1:20 pm•
• 3RD PERIOD 11;45 – 12:45 pm• 2nd LUNCH 12:50– 1:20 pm• • 4TH PERIOD 1:25 – 2:25 pm
Todays Schedule• 7:55 – 8:05 HW Review• 8:05 – 8:30 Quiz• 8:35 – 9:05 10.6 Circles, arcs, and pie charts• 9:10 – 9:35 Cumulative Review/Video• 9:40 – 10:25 Assembly
Warm-up• Get out your notes and review for a quiz
• You will need to know how to:• find the area of a
• parallelogram, triangle, trapezoid, rhombus, kite• fill in missing angles of a regular polygon• solve for the apothem, radius, and find area in a regular polygon• find ratios of area, ratios of perimeter, and similarity ratios
• HW will be stamped during the quiz
Today’s Agenda• Circles
• Semicircles• Arcs
• Minor• Major
• Arc Length• Pie Charts
• CRT
Circles• Circle – set of all points equidistant from a point
• called by center
2 feet2 fe
et
2 feet
2 feet
Circle Vocabulary
Identify the Following
• Radii• Diameter• Center• Central Angle
• angle created by 2 radii
Congruent Circles
• circles with the same radius
Central Angle
• Angle whose vertex is the center of a circle
Arc
• Arc: portion of a circle• Arc Length: length of an arc
Semicircle
• half circle• arc of 180˚
Arcs
• Minor arc• arc less than 180˚
• Major Arcarc greater than 180˚
Pie Charts
Pie Charts
Pie Charts
Percentages to Degrees
31%33%32%4%
Example 1
• Identify the following in circle O:• a)minor arcs
• b) major arcs
• c) semicircles
Arc-Addition Postulate
• Adjacent Arcs = Arcs next to each other
• The measure of an arc formed by 2 adjacent arcs is the sum of the two arcs.
• Arc AB + Arc BC = Arc AC
Example 1• Find the measure of each arc
• arc XY• arc DXM• arc XW• arc MWX• angle xcw
Arc Length• The length of an arc is
• circumference = 2πr
• Arc AB =
Example 5
• Find the arc length of ADB and AB in circle M.
• Arc ADB
• Arc AB
Assignment• 10.6 Worksheet
• Chapters 1- 10 Cumulative Review• Due on day of test