Exercise 4 Page 449

We want to find the length of the line segment JM.

In the diagram we can see that GH, JK, and MN intersect the transversal HN.Moreover, the angles they form — ∠ H, ∠ K, and ∠ N — are corresponding and congruent. Therefore, GH, JK, and MN are parallel lines. Let's recall the Three Parallel Lines Theorem.

Three Parallel Lines Theorem

If three parallel lines intersect two transversals, then they divide the transversals proportionally.

With this logic, we know that GH, JK, and MN divide GM and HN proportionally. HK/KN=GJ/JM Since we know that HK= 15, KN= 18, and GJ= 16, we can substitute these values into the above equation and solve for JM.

HK/KN=GJ/JM

SubstituteValues

Substitute values

15/18=16/JM

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Solve for JM

MultEqn

LHS * JM=RHS* JM

15/18* JM = 16

MultEqn

LHS * 18/15=RHS* 18/15

JM= 16*18/15

MoveLeftFacToNum

a*b/c= a* b/c

JM=288/15

CalcQuot

Calculate quotient

JM=19.2