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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

1. Classifying Triangles

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Exercise 45 Page 242

Use the Distance Formula.

Side Lengths: XY=2sqrt(2), YZ=2, XZ=2
Type: Isosceles

Practice makes perfect

We can use the given coordinates of the vertices and the Distance Formula to find the length of each side.

We can start with the length of XY.

XY=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

SubstitutePoints

Substitute ( 3,- 2) & ( 1,- 4)

XY=sqrt(( 1- 3)^2+( - 4-( - 2))^2)

▼

Simplify right-hand side

a-(- b)=a+b

XY=sqrt((1-3)^2+(- 4+2)^2)

Add and subtract terms

XY=sqrt((- 2)^2+(- 2)^2)

NegBaseToPosBase

(- a)^2=a^2

XY=sqrt(2^2+2^2)

Calculate power

XY=sqrt(4+4)

Add terms

XY=sqrt(8)

SplitIntoFactors

Split into factors

XY=sqrt(4 * 2)

sqrt(a* b)=sqrt(a)*sqrt(b)

XY=sqrt(4) * sqrt(2)

Calculate root

XY=2sqrt(2)

We can find the length of the other sides in the same way.

Side	Expression	Length
XY	sqrt((1-3)^2+(- 4-(- 2))^2)	XY=2sqrt(2)
YZ	sqrt((3-1)^2+(- 4-(- 4))^2)	YZ=2
XZ	sqrt((3-3)^2+(- 4-(- 2))^2)	ZX=2

Notice that two of the lengths of the sides are the same. Therefore, △ XYZ is isosceles.

Subchapter links

Check Your Understanding p.240

Practice and Problem Solving p.241-243

H.O.T. Problems p.243

Standardized Test Practice p.244

Spiral Review p.244

Skills Review p.244