Exercise 37 Page 223

When naming congruent polygons, corresponding vertices are listed in the same order. Therefore, in order to identify the congruent parts, we need to look at the order of the vertices in the congruence statement. △ A B C ≅ △ D E F We want to find BC and EF. Using the congruence statement, we have that B C ≅ E F. This implies that B C = E F. If we consider the two given equations as a system of equations, we can use this congruence relation to simplify the system. BC=3z+2 E F=z+6 ⇒ BC=3z+2 B C=z+6 Now, we can solve the system using the Substitution Method.

BC=3z+2 & (I) BC=z+6 & (II)

Substitute

(I): BC= z+6

z+6=3z+2 BC=z+6

▼

(I): Solve for z

SubEqn

(I): LHS-z=RHS-z

6=2z+2 BC=z+6

SubEqn

(I): LHS-2=RHS-2

4=2z BC=z+6

DivEqn

(I): .LHS /2.=.RHS /2.

2=z BC=z+6

RearrangeEqn

(I): Rearrange equation

z=2 BC=z+6

Now that we found the value of z, let's substitute it into the second equation to find BC.

z=2 BC=z+6

Substitute

(II): z= 2

z=2 BC= 2+6

AddTerms

(II): Add terms

z=2 BC=8

Remember that EF ≅ BC. Therefore, EF=BC=8.