1. 5-3: Medians and Altitudes of Triangles
Page 311
12)
59.7
13)
63.9
14)
62.8
15)
16)
(-2.5, 7)
17)
(-1.5, 9.5)
18)
8.37
19)
55°
22)
Angle Bisector, mBAE = mEAC
23)
Perpendicular Bisector, mBAE = mEAC
24)
Angle Bisector, mABG = mGBC
25)
Neither, no indiciation where Angle C is a bisector
26)
Neither
27)
28)
Never
29)
Sometimes
30)
31)
32)
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5-3: Medians and Altitudes of Triangles

2. Medians and Altitudes of Triangles
Section 5-3
Geometry PreAP, Revised ©2013
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5-3: Medians and Altitudes of Triangles

3. 5-3: Medians and Altitudes of Triangles
Definitions
Centroid is the balancing point or center of gravity of the triangle using the midpoint of each side and the vertex of the triangle.
The medians of a triangle intersect at a point that is two-thirds of the distance from each vertex to the midpoint of the opposite side.
The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side
Orthocenter are the three altitudes of a triangle
Altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side; the height of the triangle is the length of the altitude
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5-3: Medians and Altitudes of Triangles

4. 5-3: Medians and Altitudes of Triangles
Identify Centroid
Centroid is the balancing point or center of gravity of the triangle using the midpoint of each side and the vertex of the triangle.
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5-3: Medians and Altitudes of Triangles

5. 5-3: Medians and Altitudes of Triangles
Identify Centroid
Centroid is the balancing point or center of gravity of the triangle using the midpoint of each side and the vertex of the triangle.
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5-3: Medians and Altitudes of Triangles

6. 5-3: Medians and Altitudes of Triangles
Video of Centroid
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5-3: Medians and Altitudes of Triangles

7. 5-3: Medians and Altitudes of Triangles
Example 1
In ∆LMN, RL = 21 and SQ = 4. Find LS.
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5-3: Medians and Altitudes of Triangles

8. 5-3: Medians and Altitudes of Triangles
Example 2
In ∆LMN, RL = 21 and SQ = 4. Find RS + NQ.
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5-3: Medians and Altitudes of Triangles

9. 5-3: Medians and Altitudes of Triangles
Your Turn
In ∆JKL, ZW = 7, and LX = 8.1. Find KW.
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5-3: Medians and Altitudes of Triangles

10. 5-3: Medians and Altitudes of Triangles
Example 3
A sculptor is shaping a triangular piece of iron that will balance on the point of a cone. At what coordinates will the triangular region balance?
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5-3: Medians and Altitudes of Triangles

11. Steps in finding the Orthocenter
Graph the triangle
Write an equation from the altitude to a vertex
Write another equation from the altitude to the vertex
Create a system to determine the orthocenter
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5-3: Medians and Altitudes of Triangles

12. 5-3: Medians and Altitudes of Triangles
Identify Orthocenter
Orthocenter are the three altitudes of a triangle; Prefix: STRAIGHT
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5-3: Medians and Altitudes of Triangles

13. 5-3: Medians and Altitudes of Triangles
Altogether…
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5-3: Medians and Altitudes of Triangles

14. 5-3: Medians and Altitudes of Triangles
Identify Orthocenter
Orthocenter are the three altitudes of a triangle; Prefix: STRAIGHT
orthocenter
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5-3: Medians and Altitudes of Triangles

15. 5-3: Medians and Altitudes of Triangles
Example 4
Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1).
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5-3: Medians and Altitudes of Triangles

16. 5-3: Medians and Altitudes of Triangles
Example 4
Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1).
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5-3: Medians and Altitudes of Triangles

17. 5-3: Medians and Altitudes of Triangles
Example 4
Find the orthocenter of ∆XYZ with vertices X(3, –2), Y(3, 6), and Z(7, 1).
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5-3: Medians and Altitudes of Triangles

18. 5-3: Medians and Altitudes of Triangles
Example 5
Find the orthocenter of ∆KLM with vertices K(2, –2), L(4, 6), and M(8, –2).
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5-3: Medians and Altitudes of Triangles

19. 5-3: Medians and Altitudes of Triangles
Your Turn
Find the orthocenter of ∆PQR with vertices P(–5, 8), Q(4, 5), and R(–2, 5).
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5-3: Medians and Altitudes of Triangles

20. 5-3: Medians and Altitudes of Triangles
Assignment
Pg , odd, all Quiz BLOCK DAY
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5-3: Medians and Altitudes of Triangles