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McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

3. Tests for Parallelograms

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Exercise 51 Page 421

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

(4.5,1.5 )

Practice makes perfect

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 AC or BD. Let's substitute the coordinates of A and C into the Midpoint Formula to find the midpoint of AC.

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

SubstitutePoints

Substitute ( 2,5) & ( 7, -2)

( 2+ 7/2, 5+( -2)/2 )

a+(- b)=a-b

( 2+7/2, 5-2/2 )

Add and subtract terms

( 9/2, 3/2 )

Write as a decimal

(4.5, 1.5 )

The midpoint of AC is (4.5,1.5). Consequently, these are the coordinates of the intersection of the diagonals of the parallelogram ABCD.

Subchapter links

Check Your Understanding p.417-418

H.O.T. Problems p.420

Standardized Test Practice p.421

Spiral Review p.421

Skills Review p.421