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Section 4.7 Section 4.7 Medians, Altitudes, Medians, Altitudes, and Perpendicular and Perpendicular
BisectorsBisectorsWARM UP
Activity Part 1Activity Part 1
1)1) Draw a triangle. Draw a triangle.
2)2) Label it Label it ∆∆BOY.BOY.
3)3) Measure each side of the Measure each side of the triangle.triangle.
4)4) Find and mark the Find and mark the MIDPOINT of each side.MIDPOINT of each side.
Activity Part 2Activity Part 2
1)1) Draw a line connecting Point Draw a line connecting Point B to the MIDPOINT on the B to the MIDPOINT on the OPPOSITEOPPOSITE SIDE. SIDE.
2)2) Draw a line connecting Point Draw a line connecting Point O to the MIDPOINT on the O to the MIDPOINT on the OPPOSITEOPPOSITE SIDE. SIDE.
3)3) Draw a line connecting Point Draw a line connecting Point Y to the MIDPOINT on the Y to the MIDPOINT on the OPPOSITEOPPOSITE SIDE. SIDE.
What is a What is a MedianMedian?? A segment from a vertex to the A segment from a vertex to the
midpointmidpoint of the of the oppositeopposite side. side. – Always three medians.Always three medians.
See the medians for a given triangle.See the medians for a given triangle.
A
B
C
What is a What is a CentroidCentroid?? Centroid: the point where all three Centroid: the point where all three
medians meetmedians meet The medians of a triangle divide one The medians of a triangle divide one
another into ratios of 2:1.another into ratios of 2:1.
A
B
C
3x
11
yx = 6
y = 5.5
Activity 2Activity 2
1)1) Draw a triangle.Draw a triangle.
2)2) Label it Label it ∆∆ WIG. WIG.
3)3) Draw a segment from W to Draw a segment from W to the the oppositeopposite side so that side so that it makes a right angle with it makes a right angle with that side.that side.
What is an What is an AltitudeAltitude?? The The perpendicularperpendicular segment from a segment from a
vertex to the vertex to the oppositeopposite side. side. Altitudes can be drawn OUTSIDE of the Altitudes can be drawn OUTSIDE of the
triangle.triangle.
A
B
C
What are What are Perpendicular Perpendicular BisectorsBisectors??
A line or ray that is A line or ray that is perpendicularperpendicular to the segment at its to the segment at its midpointmidpoint. .
Does Does NOTNOT have to start at a have to start at a VERTEXVERTEX
Perpendicular BisectorsPerpendicular Bisectors What is true of What is true of ABAB and and ACAC??
XB C
A
CircumcenterCircumcenter: point where three : point where three perpendicular bisectors meet.perpendicular bisectors meet.
TOGETHER, OPEN YOUR TOGETHER, OPEN YOUR TEXTBOOKTEXTBOOK
Page 155 - Classroom ExercisesPage 155 - Classroom Exercises
#1-6#1-6