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