Exercise 7 Page 434

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

Using the Centroid Theorem, we can write an equation that we can use to find the desired lengths. SZ = 2/3SU By the Segment Addition Postulate, we can rewrite SU as the sum of the two smaller segments. We are given that ZU= 5, which we can substitute into this new equation. SU=SZ+ ZU ⇒ SU=SZ+ 5 Next, we can combine these two equations to solve for SZ.

SZ = 23SU

Substitute

SU= SZ+5

SZ = 23( SZ+5)

Distr

Distribute 2/3

SZ = 23SZ+ 103

SubEqn

LHS- 23SZ=RHS- 23SZ

13SZ = 103

MultEqn

LHS * 3=RHS* 3

SZ = 10