UNIT 7 PACKET (10.6-10.7 & Chapter 12)
DATE / LESSON / ESSENTIAL QUESTION / I WILL…. / Assignments02/06
Due: 2/10 / Lesson 10.6: Circles and Arcs / What are the parts of a circle and how can you use them? / Find the measures of central angles and arcs and find circumference and arc length. / BW:
● # 2, 3
CW/HW:
● Lesson 10.6 Notes
● WB page 277
● Page 654 #1-8
EXIT:
● Answer EQ in. COMPLETE SENTENCES!
2/07-2/08
Due: 2/10 / Lesson 10.7: Areas of Circles and Sectors / How do you find the area of a circle? / Find the areas of circles, sectors, and segments of circles. / BW:
● # 6, 11
CW/HW:
● Lesson 10.7 Notes
● WB page 281
EXIT:
● Page 663 #1-6
2/09-2/10
Due: 2/10 / Assessment / Unit 7 Assessment1
2/13
Due: 2/17 / Lesson 12.1: Tangent Lines / What are the properties of tangent lines? / Use properties of a tangent to a circle. / BW:
● # 7, 12
CW/HW:
● Lesson 12.1 Notes
● WB page 315-316 #1-18 (skip #13)
● WB page 317
EXIT:
● Page 766 #1-3, 5
2/14
Due: 2/17 / Lesson 12.2: Chords and Arcs / What are the properties of chords and arcs? / Use the properties of chords and arcs to find missing segments in a circle. / BW:
● # 16, 18
CW/HW:
● Lesson 12.2 Notes
● WB page 321
#1-5
EXIT:
● Page 776 #1-5
2/15
Due: 2/17 / Lesson 12.3: Inscribed Angles / How can you use inscribed angles to find missing angle measures? / Find the measures of inscribed angles and angles formed by tangents and chords. / BW:
● # 17
CW/HW:
● Lesson 12.3 Notes
● WB page 325
EXIT:
● Page 784 #1-5
2/17-2/17
Due: 2/17 / Assessment / Unit 7 Assessment 2
2/21 / Lesson 12.4: Chords and arcs / What are the properties of chords and arcs? / Find the measures of angles formed by chords, secants, and tangents. Find the lengths associated with circles. / BW:
● # 14
CW/HW:
● Lesson 12.4 Notes
● WB page 329
#1-6
EXIT:
● Page 794 #1-4, 7
2/22 / Lesson 12.5: Circles in the coordinate plane / How can you use the center and radius of a circle in a real-world setting? / Write an equation of a circle. Find the center and radius of a circle. / BW:
● #4, 8
CW/HW:
● Lesson 12.5 Notes
● WB page 333
EXIT:
● Page 800 #1-7
2/23-2/24
Due: 2/24 / Assessment / Unit 7 Assessment 3
CIRCLES BELL WORK
CIRCLES BELL WORK
Exit Tickets
EXIT Tickets
10.6 Circles and Arcs
(Use page 649 to fill in the blanks and diagrams.)
In a plane, a circle is the ______equidistant from a given point called the center. You name a circle by its center.
A diameter is a segment that contains the ______of a circle and has both ______on the circle. A radius is a segment that has one endpoint at the ______and the other endpoint on the ______. Congruent circles have congruent ______. A central angle is an angle whose ______is the ______of the circle.
An ______is part of a circle. One type of arc, a semicircle, is ______of a circle. A minor arc is ______than a ______. A major arc is ______than a ______. You name a minor arc by its ______and a major arc or a semicircle by its ______and another ______on the ______
Example #1: Naming Arcs
Example #2: Finding the Measures of Arcs
Find the measure of arc in R.
The circumference of a circle = ______x ______OR ____ x _____ x ______
Example #3: Finding Circumference
Find the circumference of each circle. Leave your answer in terms of π.
______
Example #4: Finding a Distance
Example #4: Finding Arc Length
Find the length of each darkened arc. Leave your answer in terms of π.
10.7: Area of Circles and Sectors
Area of a Circle = ___ x ______
Example #1: Finding the Area of a Circle
Find the area of each circle. Leave you answer in terms of pi.
/ A dog is on a leash that is attached to a pole in the ground. If the leash is 8 feet long, in how much area can the dog move around? Round to the nearest tenth.(Use page 661 to fill in the blanks and diagram.)
A sector of a circle is a ______bound by an ______of the circle and the ______to the arc’s endpoints. You name a sector using ______, the ______of the circle, and the other ______.
Example #2: Finding the Area of a Sector of a Circle
Find the area of each shaded sector of the circle. Leave you answer in terms of pi.
Example #3: Finding the Area of a Segment of a Circle
Step 1: Find the area of sector RST.
Step 2: Find the area of triangle RST.
Step 3: Subtract (step 1 answer – step 2 answer) to find the area of the segment.
12.1 Tangent Lines
Example #1: Finding Angle Measures and Finding the Radius
Find the missing angle or side.
Remember:
● Tangent lines are perpendicular to radius (so it forms a right triangle!).
● Triangles = 180
● If you know 2 sides of a right triangle, you can find the missing side using ______
Example #2: Circles Inscribed in Polygons
Step 1: Fill in the missing segments on the picture. Tangent segments that share a common endpoint are congruent. Therefore….
PX = 15 and ______= 15
RZ = 17 and ______= 17
Step 2: Make an equation and solve for x. The perimeter is 88. We know what everything equals, except for segments ______and ______. Put an x by each of them in the picture. Write your equation and solve for x.
12.2 Chords and Arcs
Chord Arc
Several relationships between chords, arcs, and the central angles of a circle are listed below. The converses of these theorems are also true.
Theorem 12-4 Congruent central angles have congruent arcs.
Theorem 12-5 Congruent central angles have congruent chords.
Theorem 12-6 Congruent chords have congruent arcs.
Theorem 12-7 Chords equidistant from the center are congruent.
Example #1: Finding the Length of a Chord
Find the value of x in the three circles below.
Theorem 12-8 In a circle, if a diameter is perpendicular to a chord, it bisects that chord and its arc. /Theorem 12-9 In a circle, if a diameter bisects a chord that is not a diameter of the circle, it is perpendicular to that chord. /
Theorem 12-10 If a point is an equal distance from the endpoints of a line segment, then that point lies on the perpendicular bisector of the segment. /
Example #2: Finding Measures in a Circle
Use the Pythagorean Theorem to find the value of x.
12.3 Inscribed Angles
Example #1: Using the Inscribed Angle Theorem
Find the value of each variable.
Hint: Angle = ½ arc OR Arc = 2 x angle
Example #2: Using Corollaries to Find Angle Measure
Find the value of each variable.
Example #3: Using Arc Measure
Find the value of each variable. Lines that appear to be tangent are tangent.
12.4 Angle Measures and Segment Lengths
Secant:
Example #1: Finding Angle Measures
Use Theorem 12-13 and 12-14 to find each variable.
Example #2: Finding Segment Lengths
Use Theorem 12-15 to find each variable.
12.5: Circles in the Coordinate Plane
Example #1: Writing the Equation of a Circle
9/5/2013