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5.3 Medians and Altitudes of a
Triangle
Use properties of medians, centroids, orthocenters, and altitudes in
triangles to find missing side lengths.
Vocabulary: median, altitude, centroid, orthocenter
Review HW: 4.2 Practice A WS
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Review HW: 4.2 Practice A WS
Wednesday’s Classwork
0 Classwork: p. 275-276 #10-17; p. 278 #27-28
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Medians
0 The median of a triangle is a line segment connecting a
vertex to the midpoint of the opposite side.
Centroid
0 The centroid is the point where all 3 medians intersect.
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Centroid
0 The distance from the vertex to the centroid is 2/3 the
length of the median.
Example #1
R is the centroid of ΔSTU. Segment SR = 16.
SV = _____
RV = _____
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Example #2
0 Find the coordinates of J, the midpoint of segment DF.
0 Find the length of the median EJ.
0 Find the coordinates of the
centroid of ΔDEF.
Altitude
0 The altitude of a triangle is a perpendicular segment from
a vertex to the opposite side.
0 We can think of the altitude as the height of the triangle.
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Altitude
The altitude isn’t always inside the triangle.
Orthocenter
0 The orthocenter is the point where the 3 altitudes of a
triangle intersect.
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Example #3
For each triangle, determine if the orthocenter is located inside or
outside of the triangle (Sketch a picture!)
a) Acute Triangle
b) Right Triangle
c) Obtuse Triangle
Example #3
For each triangle, determine if the orthocenter is located inside or
outside of the triangle (Sketch a picture!)
a) Acute Triangle
b) Right Triangle
c) Obtuse Triangle
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Practice
Complete p. 282 #1, 3-11, 17-23
HW: 5.3 Practice A WS
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