Warm Up1.Give the restrictions on the third side

of the triangle if the first two sides are 18 and 30.

2. Find x and y for both figures.

55° 70°x

y

100°2x + 10

4y

80

1

CAAG Unit 7B

UNIT QUESTION: What are the properties and characteristics of polygons?Standard: MM1G1.e.

Today’s Question:What is the centroid of a triangle, and what is special about it?Standard: MM1G.3.e.

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Special Special Segments in Segments in

TrianglesTriangles3

Median

MedianMedian

4

Altitude

AltitudeAltitude

5

Tell whether each red segment is an altitude of the triangle.The altitude is the “true height” of

the triangle.

6

Perpendicular Bisector

Perpendicular Perpendicular BisectorBisector

7

Tell whether each red segment is an perpendicular bisector of the triangle.

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Angle Bisector

Angle BisectorAngle Bisector

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Drill & Drill & PracticePractice

Indicate which special triangle segment the red line is based on the picture and markings

10

11

12

13

14

15

20 20

16

start at a vertex and bisect the opposite

side.

Median

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The intersection of the medians is called the CENTROID.

How many medians does a triangle have?

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Theorem 5.8

The length of the segment from the vertex to the

centroid is twice the length of the segment from the centroid to the midpoint.

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A BF

X

E

C

D

20

A BF

X

E

C

D

21

In ABC, AN, BP, and CM are medians.

A

B

M

P E

C

NIf EM = 3, find EC.EC = 2(3)

Ex: 1

EC = 6

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In ABC, AN, BP, and CM are medians.

A

B

M

P E

C

N

If EN = 12, find AN.AE = 2(12)=24

Ex: 2

AN = 36

AN = AE + ENAN = 24 + 12

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Altitude

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The intersection of the altitudes is called the ORTHOCENTER.

How many altitudes does a triangle have?

25

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The intersection of the perpendicular bisectors is called the CIRCUMCENTER.

How many perpendicular

bisectors does a triangle have?

27

What is special about the

CIRCUMCENTER?

Equidistant to the vertices of the triangle.

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Example 1:Point G is the circumcenter of the triangle. Find GB.

B

A

C

G

ED

F

2

5

7

7

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Angle Bisector

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The intersection of the angle bisectors is called the INCENTER.

How many angle bisectors does a triangle have?

31

What is special about the INCENTER?

Equidistant to sides of the triangle

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Example 1:

Point N is the incenter of the triangle. Find the length of segment ON.

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30 18

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Memorize these!Memorize these!

MCAOABI

PBCC

Medians/Centroid

Altitudes/Orthocenter

Angle Bisectors/Incenter

Perpendicular Bisectors/Circumcenter

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Will this work?Will this work?

MCAOABI

PBCC

My Cat

Ate Our

Apples But I

Prefer Blue Cheese Crumbles

35

Come up with your own!

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