8/9/2015 eq: what are the differences between medians, altitudes, and perpendicular bisectors?...
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![Page 1: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/1.jpg)
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
Warm-UpTake out homework p.301 (4-20) evenCheck your answers with a partner
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04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
![Page 3: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/3.jpg)
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
![Page 4: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/4.jpg)
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
![Page 5: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/5.jpg)
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
![Page 6: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/6.jpg)
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
![Page 7: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/7.jpg)
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
![Page 8: 8/9/2015 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? Warm-Up Take out homework p.301 (4-20) even Check your answers](https://reader036.vdocument.in/reader036/viewer/2022062516/56649da15503460f94a8cc30/html5/thumbnails/8.jpg)
Median
Picture: Both sides are congruent
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Median
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04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
Midpoint-If you have a midpoint- then the segments on both sides are CONGRUENT! That is why you will see the “tick marks”For the measure of the entire line- add both sides!
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M D P
N
C
In MC and ND are medians.MNP,
1. What is NC if NP = 18?
9
2. If DP = 7.5, find MP. 15
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A B C
E
D
1.What is ED if DC = 14?
2.What Is AC is BC is 9?
14
3.If BC = 3, find AC.
6
AD and EB are medians:
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So if you are given the length of the entire side, how do you find a missing segment?If you are given the length of a segment, how to you find the entire side?If you have a median- what do you know about each side?
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A E B
CD
If CD = 2x + 5, BD = 4x – 1, and AE = 5x –2, find BE.
In CE and AD are medians.ABC,
BD = CD 4x – 1= 2x + 5
2x = 6 x = 3
AE = BEBE = 5x – 2BE = 5(3) – 2
BE = 13
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The intersection of the medians is called the CENTROID.
How many medians does a triangle have?
Draw the Picture:
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When three or more lines or segments meet at the same point.
Concurrent:
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Theorem 6-1
Distance from vertex to
centroid is twice the distance from
centroid to midpoint.
Draw Picture
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EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
Vertex to Centroid LONGER Centroid to Midpoint shorter
x + 2x = whole median
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A BF
X
E
C
D
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Quick AssessmentWhat is a median?What is a centroid?What does concurrent mean?What is the vertex?What is a midpoint?
04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
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A BF
X
E
C
D
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04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
In ABC, AN, BP, and CM are medians.
A
B
M
P E
C
N
If EM = 3, find EC.
EC = 2(3)
Ex: 1
EC = 6
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04/19/23
EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
In ABC, AN, BP, and CM are medians.
A
B
M
P E
C
NIf EN = 12, find AN.AE = 2(12)=24
Ex: 2
AN = 36
AN = AE + ENAN = 24 + 12
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Altitude
Picture:
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EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
Altitude
The altitude is the “true
height” of the triangle.
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Tell whether each red segment is an altitude of the triangle.The altitude is the “true height” of
the triangle.
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Perpendicular Bisector
Picture:
Both sides are congruent- make sure you see this or it is NOT a perpendicular bisector
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Tell whether each red segment is an perpendicular bisector of the triangle.
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Can you have both?Can it be both an altitude and perpendicular bisector?
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Quick AssessmentWhat is the difference between altitude and perpendicular bisector?What is an altitude?What is a perpendicular bisector?
How can the segment be both- altitude and perpendicular bisector?
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EQ: What are the differences between medians, altitudes, and perpendicular bisectors?
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Angle bisector of a triangle : is the bisector of each angle of the triangle. (cuts each angle in
half)
Incenter of the triangle: where the angle bisectors meet.
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Angle Bisectors
Incenter
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Concurrency of AngleBisectors of a Triangle
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
B
F
A
D
P
E
C
PD = PE = PF