Exercise 16 Page 259

The order of the vertices in the given congruence statement tells us which vertices correspond in the polygons. Let's use colors to illustrate this. B C DE ≅ R S TU

By the order of the vertices in the names of the polygons, we can tell which segments are corresponding segments.

In congruent polygons, the corresponding segments are congruent, so they have the same measure. This allows us to set up and solve an equation for w.

BC=RS

SubstituteII

BC= 4w-7, RS= 2w+13

4w-7= 2w+13

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Solve for w

SubEqn

LHS-2w=RHS-2w

2w-7=13

AddEqn

LHS+7=RHS+7

2w=20

DivEqn

.LHS /2.=.RHS /2.

w=10