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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 2 Page 467

The centroid is the point of concurrency of the medians of a triangle. Use the Concurrency of Medians Theorem.

KH = 8

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

Let's first find DH. Using the Concurrency of Medians Theorem, we can write the following equation. DK = 2/3DH We are given that DK= 16. Let's substitute it and find DH.

DK = 2/3DH

DK= 16

16=2/3DH

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Solve for DH

LHS * 3=RHS* 3

48 = 2 DH

.LHS /2.=.RHS /2.

24 =DH

Rearrange equation

DH=24

With the Segment Addition Postulate, we can rewrite DH as the sum of the two smaller segments. DH = DK+KH Now that we know DH and DK, we can find KH.

DH = DK+KH

DK= 16, DH= 24

24 = 16+KH

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Solve for KH

LHS-16=RHS-16

8 =KH

Rearrange equation

KH=8