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McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
2. Medians and Altitudes of Triangles
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Exercise 54 Page 343

Calculate the slopes of the lines using the Slope Formula.

Are the Lines Parallel, Perpendicular, or Neither? Parallel
Graph:

Practice makes perfect

In order to determine the relationship between the lines, let's calculate each of their slopes.

Slope of RS

We are given the points R(1,1) and S(9,8), which lie on RS. Let's substitute them into the Slope Formula and calculate the slope.

m_1=y_2-y_1/x_2-x_1
SubstitutePoints

Substitute ( 1,1) & ( 9,8)

m_1=8- 1/9- 1
SubTerms

Subtract terms

m_1=7/8

Slope of JK

Similarly, by substituting the points J(- 6,1) and K(2,8) into the Slope Formula, we can calculate the slope of JK.

m_2=y_2-y_1/x_2-x_1
SubstitutePoints

Substitute ( - 6,1) & ( 2,8)

m_2=8- 1/2-( - 6)
SubNeg

a-(- b)=a+b

m_2=8-1/2+6
AddSubTerms

Add and subtract terms

m_2=7/8

Analyze the Slopes

Now that we know the slopes of the lines, we can determine whether they are parallel, perpendicular, or neither. Remember that parallel slopes are the same and perpendicular slopes are opposite reciprocals. m_1=7/8 m_2=7/8 These slopes are the same, so the lines are parallel.

Graph

Let's graph the lines to verify that they are parallel. We do can this by plotting the points and drawing lines through them.

As we can see, the lines are truly parallel.

Subchapter links expand_more
arrow_right Check Your Understanding p.339
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Check Your Understanding 4 (Page 339)
arrow_right Practice and Problem Solving p.340-342
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Practice and Problem Solving 11 (Page 340)
Practice and Problem Solving 12 (Page 340)
Practice and Problem Solving 13 (Page 340)
Practice and Problem Solving 14 (Page 340)
Practice and Problem Solving 15 (Page 340)
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Practice and Problem Solving 20 (Page 340)
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Practice and Problem Solving 25 (Page 341)
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Practice and Problem Solving 28 (Page 341)
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Practice and Problem Solving 33 (Page 341)
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Practice and Problem Solving 36 (Page 342)
arrow_right H.O.T. Problems p.342
H.O.T. Problems 37 (Page 342)
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H.O.T. Problems 39 (Page 342)
H.O.T. Problems 40 (Page 342)
H.O.T. Problems 41 (Page 342)
H.O.T. Problems 42 (Page 342)
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arrow_right Standardized Test Practice p.343
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Standardized Test Practice 46 (Page 343)
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arrow_right Spiral Review p.343
Spiral Review 48 (Page 343)
Spiral Review 49 (Page 343)
Spiral Review 50 (Page 343)
Spiral Review 51 (Page 343)
Spiral Review 52 (Page 343)
Spiral Review 53 (Page 343)
Spiral Review 54 (Page 343)
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arrow_right Skills Review p.343
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