lesson 11.1 introducing circles answers · introducing circles lesson 11.1 unit 6 workbook page 7....

(Page 7)

INTRODUCING CIRCLES Lesson 11.1

Unit 6 Workbook Page 7

Greek mathematician Euclid, (often referred to as the "Father

of Geometry"), created what is know as Euclidean geometry.

He basically took ideas that people thought might always be

true and proved beyond a doubt that they were definitely

true. What we study from geometry this year is based on

Euclid's ideas.

Today, we will explore and apply some properties of circles including proving

all circles are similar using a variation of Archimedes' method.

Archimedes, another Greek mathematician, built upon Euclid's

ideas to form the foundations for Calculus. He is also credited

for coming up with the most accurate approximation of pi.

Today's Objectives ~

By the end of the lesson you should be able to:

• Label circles, arcs, and angles on a circle.

• Explain why all circles are similar.

• Explain the relationships among inscribed angles, central

angles, and intercepted arcs on a circle.

What is a circle?

What is a diameter? a radius? a chord?

What is the circumference?

What is pi?

A

What is a semicircle?

Give an example of one on the circle.

What is an arc?

Give an example of an arc on the circle.

Think about how you defined a semicircle. What do you think a major arc and

a minor arc would be? Give examples of these on the circle.

Why do we need 3 letters when we name a major arc?

A central angle is:

An inscribed angle is:

An intercepted arc is:

Do you think there is a relationship between the central angle and the inscribed

angle with the same intercepted arc?

Does that mean there is a relationship between the incribed angle and the central

with the same intercepted arc?

This means that the measure of the central angle is double the measure

of the inscribed angle of the same intercepted arc.

What can you tell me

about ∠� and ∠�?

What can you tell me

about ∠�?

Are all circles similar?

2 5

(Instead of example 2)

What is the circumference of each circle?

Ratios:

Have you ever dropped a rock in a pond? What happens

on the surface of the water?

These are called concentric circles. What is the same about

concentric circles? What is different?

Example 3 (page 10):

Example 4 (page 10):

To start with, how does the

measure of ����� compare

to the measure of ∠��?

So how does this relate to

∠��?

Example 5 (page 10):

ASSIGNMENT 11.1

WB: Page 13 # 1-10

RB: Page U6-18: # 1-10 (you need to draw the circles on your paper)