Exercise 9 Page 312

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

Using the Concurrency of Medians Theorem, we can write an equation that we can use to find one of the desired lengths, ZU. YU = 2/3ZU Since we know that YU= 9, we can solve the above equation for ZU.

9=2/3ZU

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Solve for ZU

MoveRightFacToNum

a/c* b = a* b/c

9=2ZU/3

MultEqn

LHS * 3=RHS* 3

27=2ZU

DivEqn

.LHS /2.=.RHS /2.

13.5=ZU

RearrangeEqn

Rearrange equation

ZU=13.5

With the Segment Addition Postulate, we can rewrite ZU as the sum of the two smaller segments. YU+ZY=ZU Since we know that YU= 9 and ZU = 13.5, we can solve the above equation for ZY. 9+ZY= 13.5 ⇒ ZY=4.5