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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

2. Parallelograms

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Exercise 21 Page 490

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

(5/2,5/2 )

Practice makes perfect

We are asked to find the coordinates of the intersection of the diagonals of a polygon. Let's plot the given points and draw the parallelogram with its diagonals on a coordinate plane.

The diagonals of a parallelogram will always bisect each other. Therefore, to find the coordinates of the intersection of the diagonals, we can find the midpoint of either WY or XZ. Let's substitute the coordinates of W and Y into the Midpoint Formula to find the midpoint of WY.

( x_1+x_2/2, y_1+y_2/2 )

SubstitutePoints

Substitute ( -1, 7) & ( 6, -2)

( -1+ 6/2, 7+( -2)/2 )

a+(- b)=a-b

( -1+6/2, 7-2/2 )

Add and subtract terms

( 5/2, 5/2 )

The midpoint of WY is ( 52, 52). Consequently, these are the coordinates of the intersection of the diagonals of the parallelogram WXYZ.

Extra

Properties of Parallelograms

If a quadrilateral is a parallelogram then it has the following properties.

Both pairs of opposite sides are parallel.
Opposite sides are congruent as well as opposite angles.
Consecutive angles are supplementary.
Diagonals bisect each other.
Each diagonal separates the parallelogram into two congruent triangles.

Subchapter links

Exercises p.489-493