Exercise 9 Page 358

To see whether △ MNO and △ QRS are congruent or not, let's find the length of the sides. First we can graph both triangles on the same coordinate plane using the given vertices.

Since we know the coordinates of the vertices, we can use the Distance Formula to find the length of the sides. Let's start with finding MN.

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

SubstitutePoints

Substitute ( 0,-1) & ( -1,-4)

MN=sqrt(( -1- 0)^2+( -4-( -1))^2)

▼

Simplify right-hand side

SubNeg

a-(- b)=a+b

MN=sqrt((-1-0)^2+(-4+1))^2)

SubTerms

Subtract terms

MN=sqrt((-1)^2+(-3)^2)

CalcPow

Calculate power

MN=sqrt(1+9)

AddTerms

Add terms

MN=sqrt(10)

We can find the length 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((-1-0)^2+(-4-(-1))^2) ? = sqrt((4-3)^2+(-4-(-3))^2)	sqrt(10)≠ sqrt(2)
NO and RS	sqrt((-4-(-1))^2+(-3-(-4))^2) ? = sqrt((3-4)^2+(3-(-4))^2)	sqrt(10)≠ sqrt(50)
OM and SQ	sqrt((0-(-4))^2+(-1-(-3))^2) ? = sqrt((3-3)^2+(-3-3)^2)	sqrt(20)≠ sqrt(36)

Since none of the side lengths of △ MNO match any of the side lengths of △ QRS, the triangles are not congruent. △ MNO≆△ QRS