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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Mid-Chapter Quiz

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Exercise 21 Page 41

If three points are on a straight line, we can use the Segment Addition Postulate to calculate the total length of the segment.

AD=34

Practice makes perfect

The length AD is the total length of the segment, AD.

From the figure, we can see that point C is a midpoint between A and D. This means that we can equate AC and DC to solve for x.

AC = DC

AC= 4x+5, DC= 3x+8

4x+5 = 3x+8

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Solve for x

LHS-5=RHS-5

4x=3x+3

LHS-3x=RHS-3x

x=3

Having solved the equation, we can calculate the individual lengths by substituting x= 3 into the expressions for both lengths. AC &: 4( 3)+5=17 DC &: 3( 3)+8=17 Because point C is on a straight line between A and D, we can use the Segment Addition Postulate to write an expression for the total length. We will add the lengths AC and CD to get AD.

AD = AC + DC

AC= 17, DC= 17

AD = 17 + 17

Add terms

AD = 34