Exercise 8 Page 358

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

Yes, see solution.

Practice makes perfect

Let's begin by plotting both triangles in one coordinate plane using the given coordinates. It appears that the triangles have the same shape.

To determine whether △ MNO and △ QRS are congruent or not, let's find the lengths of their sides. Since we know the coordinates of the vertices, we can use the Distance Formula to find each side length. Let's start with finding MN.

MN=sqrt((x_N-x_M)^2+(y_N-y_M)^2)

SubstitutePoints

Substitute ( 2,5) & ( 5,2)

MN=sqrt(( 5- 2)^2+( 2- 5)^2)

▼

Simplify right-hand side

SubTerms

Subtract terms

MN=sqrt(3^2+(-3)^2)

CalcPow

Calculate power

MN=sqrt(9+9)

AddTerms

Add terms

MN=sqrt(18)

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. △ MNO? ≅△ QRS 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
MN and QR	sqrt((5-2)^2+(2-5)^2)? = sqrt((-7-(-4))^2+(1-4)^2)	sqrt(18)= sqrt(18)
NO and RS	sqrt((1-5)^2+(1-2)^2)? = sqrt((-3-(-7))^2+(0-1)^2)	sqrt(17)= sqrt(17)
OM and SQ	sqrt((2-1)^2+(5-1)^2)? = sqrt((-4-(-3))^2+(4-0)^2)	sqrt(17)= sqrt(17)

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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