CONSTRUCTIONS Lesson 11.4

Unit 6 WB Page 45

(Skip question 1)

WARM-UP! (Page 45)

Each picture has a ray drawn in a triangle - can you given the specific name of each

ray based on the marks in each picture? LESSON 11.4

Review: Do you remember the names of the line segments inside these triangle?

What is a point of concurrency?

Which one of the two types of segments above does not have a point of

concurrency?LESSON 11.4

Review:When we draw three medians in a triangle, the point of concurrency is called the

___________________. This point is always inside the triangle and is the balancing

point of the triangle - the true center of the mass.

LESSON 11.4

Review:When we draw three altitudes in a triangle, the point of concurrency is called the

______________________.

This point is only inside the triangle if the triangle is acute.

If the triangle is obtuse or right, the point of concurrency is not inside the triangle.

LESSON 11.4

Review: Orthocenters

Acute Triangle

Right Triangle - The orthocenter is

on the triangle at the right angle.

Obtuse Triangle - The orthocenter is

outside the triangle.

LESSON 11.4

Review:

Today we will be using angle bisectors and perpendicular bisectors so

let's review those.

What is an Angle Bisector?

What is a Perpendicular Bisector?

LESSON 11.4

Angle bisectors are always inside the triangle, and the name of their point

of concurrency is the __________________________. This point is

important because it is the center of a circle inscribed in a triangle which

we will see later.

LESSON 11.4

LESSON 11.4

Review:

The point of concurrency of perpendicular bisectors in a triangle is called the

_______________________________. This point is important because it is the

center of a circle circumscribed about a triangle which we will also see later.

Like the orthocenter, this point is not always inside the triangle. In an obtuse triangle

it is ____________________________. In a right triangle, it is

___________________________________________.

Review: Circumcenters

LESSON 11.4

Acute Triangle

Right Triangle

Obtuse Triangle

LESSON 11.4

Today's Objectives ~

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

• Understand the purpose of locating the incenter or

circumcenter of a triangle.

• Locate the incenter or circumcenter of a triangle and use

them to draw circles.

• Explain where we use incenters and circumcenters in real life

situations.

LESSON 11.4

Where can we use "incenters" in real life? Problem #5 (page 52( on your homework

today is a great example of when it can be used.

Let's explore how to find an

incenter so you can find the

solution to this real world

problem.

LESSON 11.4

Patty Paper Activity:

Angle Bisectors & Incenters

More Words to Know:

Inscribed Circle

Circumscribed Triangle

LESSON 11.4

Let's use a compass to do Example 3 (page 48):

LESSON 11.4

Task (page 49):

LESSON 11.4

Task 2/coaching (page 49):

LESSON 11.4

Patty Paper Activity:

Perpendicular Bisectors & Circumcenters

More Words to Know:

Circumscribed Circle

Inscribed Triangle

Page 58

LESSON 11.4

Let's use a compass to do Example 3 (page 60):

LESSON 11.4

Task (page 61):

LESSON 11.4

Task w/coaching (page 61):

LESSON 11.4

Task w/coaching (page 61):

ASSIGNMENT 11.4

WB:

Page 51 # 1-6, and

Page 63 # 1-7

LESSON 11.4