Exercise 11 Page 358

To see whether the triangles △ MNO and △ QRS are congruent or not, let's find the length of the sides.

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 ( 4,7) & ( 5,4)

MN=sqrt(( 5- 4)^2+( 4- 7)^2)

▼

Simplify right-hand side

SubTerms

Subtract terms

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

NegBaseToPosBase

(- a)^2=a^2

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 similarly. 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 Segments	Lengths	Result
MN and QR	sqrt((5-4)^2+(4-7)^2)? = sqrt((3-2)^2+(2-5)^2)	sqrt(10)= sqrt(10)
NO and RS	sqrt((2-5)^2+(3-4)^2)? = sqrt((0-3)^2+(1-2)^2)	sqrt(10)= sqrt(10)
OM and SQ	sqrt((4-2)^2+(7-3)^2)? = sqrt((2-0)^2+(5-1)^2)	sqrt(20)= sqrt(20)

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