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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Medians and Altitudes of Triangles

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Exercise 6 Page 422

The centroid is the point of concurrency for the medians of a triangle. Use the Centroid Theorem.

6

Practice makes perfect

The centroid is the point of concurrency for the medians of a triangle. In the given diagram, J is the centroid.

Using the Centroid Theorem, we can write an equation that we can use to find the desired lengths. SJ = 2/3SV By the Segment Addition Postulate, we can rewrite SV as the sum of the two smaller segments. SV=SJ+VJ We are given that VJ=3. Let's substitute both of these into the first equation to find the length of SJ.

SJ = 2/3SV

SV= SJ+VJ

SJ = 2/3( SJ+ VJ)

VJ= 3

SJ = 2/3(SJ+ 3)

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Solve for SJ

Distribute 2/3

SJ = 2/3SJ+2

LHS-2/3SJ=RHS-2/3SJ

1/3 SJ=2

LHS * 3=RHS* 3

SJ=6

Subchapter links

Exercises p.421-425