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

OrthocenterOrthocenter: point where : point where three altitudes meetthree altitudes meet

Which line is the median?

Which line is the altitude?

a

b

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

Partner PracticePartner Practice

Page 157 # 19 (a, b, and c) Page 157 # 19 (a, b, and c)

TO BE HANDED IN! Make it neat.TO BE HANDED IN! Make it neat.

I only need one per group.I only need one per group.