Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
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Exercise 8 Page 425

Review the classifications of quadrilaterals.

x=6
y=5

Practice makes perfect

Let's review the classifications of quadrilaterals.

Quadrilateral Definition Properties
Parallelogram Both pairs of opposite sides are parallel.
  • Opposite sides are congruent.
  • Consecutive angles are supplementary.
  • Opposite angles are congruent.
  • Diagonals bisect each other.
Rhombus Parallelogram with four congruent sides.
  • Diagonals are perpendicular.
  • Each diagonal bisects a pair of opposite angles.
Rectangle Parallelogram with four right angles.
  • Diagonals are congruent.
Isosceles trapezoid Trapezoid with legs that are congruent.
  • Diagonals are congruent.
Kite Quadrilateral with two pairs of consecutive congruent sides and no opposite congruent sides.
  • Diagonals are perpendicular.

Now let's take a look at the given figure.

In the given quadrilateral, both pairs of opposite sides are parallel, which makes it a parallelogram. We know that the diagonals of a parallelogram bisect each other.

Using that information, we can write corresponding equations. l4x-4=3x+2 2y+2=2x We see that x appears in both equations and y appears only in the second one. Therefore, let's solve the first equation to find x.
4x-4=3x+2
4x=3x+6
x=6
We can now substitute x= 6 into the second equation to find y.
2y+2=2x
2y+2=2( 6)
2y+2=12
2y=10
y=5
We found that x=6 and y=5.