constructions lesson 11.4 unit 6 wb page...
TRANSCRIPT
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CONSTRUCTIONS Lesson 11.4
Unit 6 WB Page 45
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(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
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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
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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
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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
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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
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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
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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
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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
___________________________________________.
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Review: Circumcenters
LESSON 11.4
Acute Triangle
Right Triangle
Obtuse Triangle
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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.
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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.
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LESSON 11.4
Patty Paper Activity:
Angle Bisectors & Incenters
More Words to Know:
Inscribed Circle
Circumscribed Triangle
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LESSON 11.4
Let's use a compass to do Example 3 (page 48):
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LESSON 11.4
Task (page 49):
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LESSON 11.4
Task 2/coaching (page 49):
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LESSON 11.4
Patty Paper Activity:
Perpendicular Bisectors & Circumcenters
More Words to Know:
Circumscribed Circle
Inscribed Triangle
Page 58
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LESSON 11.4
Let's use a compass to do Example 3 (page 60):
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LESSON 11.4
Task (page 61):
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LESSON 11.4
Task w/coaching (page 61):
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LESSON 11.4
Task w/coaching (page 61):
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ASSIGNMENT 11.4
WB:
Page 51 # 1-6, and
Page 63 # 1-7
LESSON 11.4