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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

Chapter Review

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Exercise 39 Page 424

Find the lengths of the sides of the triangle by using the Distance Formula.

Isosceles

Practice makes perfect

Let's label the given triangle's vertices A, B, and C.

Now we will classify it as scalene, isosceles, or equilateral.

Classifying the Triangle

Let's begin by reviewing the definitions of a scalene, isosceles, and equilateral triangles.

Scalene: a triangle with three sides all of different lengths.
Isosceles: a triangle with two sides of equal length.
Equilateral: a triangle with all sides of equal length.

To classify our triangle we will find the length of each side using the Distance Formula.

Side	Distance Formula	Simplified
Length of AB: ( 0,2), ( 3,3)	sqrt(( 3- 0)^2+( 3- 2)^2)	sqrt(10)
Length of BC: ( 3,3), ( 1,-1)	sqrt(( 1- 3)^2+( -1- 3)^2)	sqrt(20)
Length of CA: ( 1,-1), ( 0,2)	sqrt(( 0- 1)^2+( 2-( -1))^2)	sqrt(10)

As we can see, two sides of our triangle has the same length. Therefore, it is an isosceles triangle.

Subchapter links

Exercises p.420-424