5.1 Bisectors of Triangles supplemental lesson€¦ · 5.1 Bisectors of Triangles supplemental...
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GHLesson 52_notes.notebook October 30, 2015 A B C J K L P Q R S T 5.1 Bisectors of Triangles supplemental lesson
Transcript of 5.1 Bisectors of Triangles supplemental lesson€¦ · 5.1 Bisectors of Triangles supplemental...
GHLesson 52_notes.notebook October 30, 2015
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J K
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5.1 Bisectors of Triangles supplemental lesson
GHLesson 52_notes.notebook October 30, 2015
The median of a triangle is a segment whose endpoints are a vertex and the midpoint of an opposite side of the triangle.
5.2 Medians and Altitudes of Triangles
Students will be able to . . .
• identify and use medians in triangles
• identify and use altitudes
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B
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Add the medians from A and C
GHLesson 52_notes.notebook October 30, 2015
The three medians of a triangle intersect at a single point called the centroid.
For all triangles, the centroid is inside of the triangle.
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X
The centroid divides the median into two segements.
Vertex to centroid
Centroid to midpoint
Vertex
Midpoint
CentroidThe lengths of the two segments are related to each other and the length of the median.
GHLesson 52_notes.notebook October 30, 2015
23
(vertex to centroid) = (length of median)
13
(midpoint to centroid) = (length of median)
Segment length relationships:
Vertex
Midpoint
Centroid
Length of median = 12
Vertex to centroid =
Length of median = 18
Midpoint to centroid =
Vertex
Midpoint
Centroid
Midpoint to centroid = 7
Length of median =
Vertex
Midpoint
Centroid
GHLesson 52_notes.notebook October 30, 2015
vertex to = 2( midpoint to centroid ) centroid( )Midpoint to centroid = 8
Vertex to centroid =
Vertex to centroid = 22
Midpoint to centroid =
Vertex
Midpoint
Centroid
Vertex
Midpoint
Centroid
Vertex to centroid = 14
Centroid to Midpoint =
Median =
GHLesson 52_notes.notebook October 30, 2015
GHLesson 52_notes.notebook October 30, 2015
An altitude of a triangle is the perpendicular segment from a vertex of the triangle to the line containing the opposite side of the triangle.
The altitude may be inside or outside of a triangle, or it may be a side of the triangle.
What type of segment is QT in the triangle?
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GHLesson 52_notes.notebook October 30, 2015
When would an altitude of a triangle be a side of the triangle?
The altitude does not have to be a vertical segment.
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GHLesson 52_notes.notebook October 30, 2015
Find the centroid of ΔFGH.
