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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 9 Page 397

Calculate the lengths of the sides of the triangles using the Distance Formula.

Yes, see solution.

To see whether △ TJD and △ SEK are congruent or not, let's find the lengths of the sides.

Since we know the coordinates of the vertices, we can use the Distance Formula. Let's start with finding TJ.

TJ=sqrt((x_J-x_T)^2+(y_J-y_T)^2)

SubstitutePoints

Substitute ( - 4,- 2) & ( 0,5)

TJ=sqrt(( 0-( - 4))^2+( 5-( - 2))^2)

▼

Simplify right-hand side

a-(- b)=a+b

TJ=sqrt((0+4)^2+(5+2)^2)

Add terms

TJ=sqrt(4^2+7^2)

Calculate power

TJ=sqrt(16+49)

Add terms

MN=sqrt(65)

We can find the lengths of the other sides in a similar way. Before we find the lengths, notice that the exercise asks about the congruence in a specific order. △ TJD ? ≅△ SEK This means that we need to check the lengths between the corresponding sides to see if each segment is congruent.

Corresponding Sides	Distance Formula	Result
TJ and SE	sqrt((0-(- 4))^2+(5-(- 2))^2) ? = sqrt((3-(- 1))^2+(10-3)^2)	sqrt(65)= sqrt(65)
JD and EK	sqrt((1-0)^2+(- 1-5)^2) ? = sqrt((4-3)^2+(4-10)^2)	sqrt(37)= sqrt(37)
DT and KS	sqrt((- 4-1)^2+(- 1-(- 2))^2) ? = sqrt((- 1-4)^2+(3-4)^2)	sqrt(26)= sqrt(26)

Since all three side pairs are congruent, the Side-Side-Side (SSS) Congruence Postulate guarantees that the triangles are congruent. △ MNO≅△ QRS

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