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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

5. Indirect Proof

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Exercise 40 Page 322

Use the Distance Formula to find the lengths of each side.

Ordered Sides: AB, BC, CA
Graph:

Practice makes perfect

To compare the side lengths of the triangle, we first need to graph the given vertices, A(3,0), B(4,3), and C(8,0). Then we can connect the vertices with straight lines.

We will find the length of each side using the Distance Formula. Let's start with finding the length of AB. The endpoints of AB are A( 3, 0) and B( 4, 3).

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

SubstitutePoints

Substitute ( 3,0) & ( 4,3)

AB=sqrt(( 4- 3)^2+( 3- 0)^2)

▼

Calculate AB

Subtract terms

AB=sqrt(1^2+3^2)

Calculate power

AB=sqrt(1+9)

Add terms

AB=sqrt(10)

Calculate root

AB=3.16227766017...

Round to 1 decimal place(s)

AB ≈ 3.2

Let's repeat this procedure for other sides

Points	Distance Formula	Approximate Value
A( 3, 0) and B( 4, 3)	AB = sqrt(( 4- 3)^2+( 3- 0)^2)	3.2
B( 4, 3) and C( 8, 0)	BC = sqrt(( 8- 4)^2+( 0- 3)^2)	5
C( 8, 0) and A( 3, 0)	CA=sqrt(( 8- 3)^2 + ( 0- 0)^2)	5

Knowing the lengths of each side, we can order them from shortest to longest. Notice that this triangle has two sides that are congruent. 3.2 < 5 ≤ 5 ⇓ AB < BC ≤ CA

Subchapter links

Lesson Check p.319

Practice and Problem-Solving Exercises p.319-322

Standardized Test Prep p.322

Mixed Review p.322