Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Review
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Exercise 15 Page 421

Recall the theorem, which tells us that if a quadrilateral is a parallelogram then its opposite sides are congruent.

x= 3
y=7

Practice makes perfect

We want to find the values of x and y for which ABCD is a parallelogram, using the given algebraic expressions for the segment lengths.

Recall the theorem that tells us that if a quadrilateral is a parallelogram then its opposite sides are congruent. Therefore, the following segments are congruent. AB ≅ CD and BC ≅ DA By the definition of congruent segments, we can conclude that their lengths are equal. AB = CD and BC = DA Let's create a system of equations by substituting the lengths of the segments into these equations. 2y=5x-1 y+3=2x+4 To solve it we will use the Substitution Method.
2y=5x-1 & (I) y+3=2x+4 & (II)
2y=5x-1 y=2x+1
2( 2x+1)=5x-1 y=2x+1
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(I): Solve for x
4x+2=5x-1 y=2x+1
2=x-1 y=2x+1
3=x y=2x+1
x=3 y=2x+1
Now that we have found x, we can substitute it in the second equation to find y.
x=3 & (I) y=2x+1 & (II)
x=3 y=2( 3)+1
x=3 y=6+1
x=3 y=7