Exercise 34 Page 401

To determine if the segments are congruent, we need to find their lengths using the Distance Formula. Let's take a look at these one at a time.

EF

The coordinates of the endpoints are E(1,4) and F(5,1).

EF = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( 1,4) & ( 5,1)

EF=sqrt(( 5- 1)^2+( 1- 4)^2)

▼

Evaluate

SubTerms

Subtract terms

EF=sqrt(4^2+(- 3)^2)

CalcPow

Calculate power

EF=sqrt(16+9)

AddTerms

Add terms

EF=sqrt(25)

CalcRoot

Calculate root

EF=5

The length of EF is 5.

GH

The coordinates of the endpoints are G(- 3,1) and H(1,6).

GH = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( - 3,1) & ( 1,6)

GH=sqrt(( 1-( - 3))^2+( 6- 1)^2)

▼

Evaluate

SubNeg

a-(- b)=a+b

GH=sqrt((1+3)^2+(6-1)^2)

AddSubTerms

Add and subtract terms

GH=sqrt(4^2+5^2)

CalcPow

Calculate power

GH=sqrt(16+25)

AddTerms

Add terms

GH=sqrt(41)

UseCalc

Use a calculator

GH=6.40312...

RoundDec

Round to 1 decimal place(s)

GH≈ 6.4

The length of GH is about 6.4.

Conclusion

The lengths are not equal, so the segments are not congruent. Since 5 is less than 6.4, we know that the length EF is less than the length GH. EF< GH

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EF

GH

Conclusion