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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

3. Proving Triangles Congruent-SSS, SAS

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Exercise 10 Page 358

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

No, see solution.

Practice makes perfect

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 ( 0,-3) & ( 1,4)

MN=sqrt(( 1- 0)^2+( 4-( - 3))^2)

▼

Simplify right-hand side

a-(- b)=a+b

MN=sqrt((1-0)^2+(4+3)^2)

Add and subtract terms

MN=sqrt(1^2+7^2)

Calculate power

MN=sqrt(1+49)

Add terms

MN=sqrt(50)

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 SQ	sqrt((1-0)^2+(4-(- 3))^2)? = sqrt((4-9)^2+(-1-(-1))^2)	sqrt(50)≠ 5
NO and QR	sqrt((3-1)^2+(1-4)^2)? = sqrt((6-4)^2+(1-(-1))^2)	sqrt(13)≠ sqrt(8)
OM and RS	sqrt((0-3)^2+(-3-1)^2)? = sqrt((9-6)^2+(-1-1)^2)	sqrt(5)≠ sqrt(13)

Since none of the side lengths of triangle △ MNO match any of the side lengths of triangle △ QRS, the SSS congruence is not met. Therefore, the triangles are not congruent. △ MNO≆△ QRS

Subchapter links

Exercises p.357-361