Discovering Geometry Chapter 6

Lesson 1: 6.5, 6.6, 6.7

Lesson 2: 6.1, 6.2, 6.3

Review

Warm-Up

Work with your tablemates to complete the 1st six definitions.

– (Consult your 1.6/1.7 notes for help.)

For each definition, make a sketch on the circle provided in your notes.

Warm Up Review

Congruent Circles: Two circles with the same ____________________.

Concentric Circles: Circles with the same ____________________.

Chord: A segment from one ________ on the circle to another ________ on the circle.

radius

center

point

point

Radius: The distance from the ____________ to a ____________ on the circle. _____ times the radius equals the __________.

Diameter: A chord which passes through the __________________ of the circle.

Tangent: A line which touches the circle at

only one __________________.

Warm Up Review center

point 2

diameter

center

point

line

Review of Shapes

http://www.youtube.com/watch?v=GiMwcxaFsIY

In this lesson we will answer…

What are the important definitions for circles?

How do I find the circumference of a circle?

What is an arc?

How can I figure out how long an arc is?

Lesson 1: 6.5, 6.6, 6.7

Secant: A __________ that ____________ a circle at _______________.

Central Angle: Angle whose vertex is the _________________of the circle.

Arc: Two ______________ on a circle and the ______________ part of the circle ______________ them.

More Definitions

line intersects

two points

center

points

line

between

Semicircle: An arc whose endpoints are the ________________ of the diameter. It measures exactly ______________ degrees.

Minor Arc: An arc of a circle that is ________________ than a semicircle. It measures ________________ degrees.

Major Arc: An arc of a circle that is ________________ than a semicircle. It measures ________________ degrees.

endpoints

180

less than

less than 180

more than 180

more than

1. Chord:

2. Radius:

3. Diameter:

4. Tangent:

5. Secant:

6. Central Angle:

7. Arc:

8. Semicircle:

9. Minor Arc:

10. Major Arc:

Practice

B

D

P

E

A

F

C

Parts of a Circle

Chords, Tangents, and Secants

Identify the appropriate segment.

Make sure you use appropriate notation!

MORE Practice

Circumference

Measuring the ____________ of the circle.

Formulas:

C = 2πr or C = πd

– where r is the ____________ and d is the ____________.

Exact circumference has _____ in the answer.

Approximate circumference is expressed as a ____________.

outside

π

diameter

decimal

radius

Using Circumference

Using Circumference

Circumference and Area of Circles

Match the circumference to the correct radius.

Use 3.14 for π

Circumference Practice

Arc Length Conjecture

The length of an arc equals _____________ _______________________________________________________.

circumference

times the measure of the central angle

divided by 360°

Length of Arc

2 or 360 360

arc arcr d

Practice

Practice

Arc Length

Calculate arc length.

Round answers to the nearest hundredths place. (Two numbers after the decimal point!)

Use 3.14 for π

Arc Length Practice

Clear Your Calculator and Turn It Off

– 2nd + 7 1 2 then 2nd On

Take out your agenda – copy down due dates

– Quizzes

– Tests

Homework

– Sections 6.5 – 6.7 (BOTH SIDES!)

Do NOT pack up until you are told to do so!

Almost Finished…