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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Tests for Parallelograms

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Exercise 7 Page 500

If both diagonals have common midpoint, then the quadrilateral is a parallelogram.

Graph:

Is It a Parallelogram? Yes.

Practice makes perfect

Let's plot the given points and draw the quadrilateral on a coordinate plane. Then we can determine whether or not it is a parallelogram using the Midpoint Formula.

If both diagonals have the same midpoint, then the quadrilateral is a parallelogram. We will consider the midpoint of WY and the midpoint of ZX and check whether they are the same. Let's calculate the midpoint of WY.

M(x_W+x_Y/2,y_W+y_Y/2)

SubstitutePoints

Substitute ( - 5,4) & ( 1,- 3)

M(- 5+ 1/2,4+( - 3)/2)

▼

Simplify

a+(- b)=a-b

M(- 5+1/2,4-3/2)

Add and subtract terms

M(- 4/2,1/2)

MoveNegNumToFrac

Put minus sign in front of fraction

M(-4/2,1/2)

Calculate quotient

M(- 2,1/2)

Now let's calculate the midpoint of ZX.

M(x_Z+x_X/2,y_Z+y_X/2)

SubstitutePoints

Substitute ( - 7,- 3) & ( 3,4)

M(- 7+ 3/2,- 3+ 4/2)

▼

Simplify

Add terms

M(- 4/2,1/2)

Calculate quotient

M(- 2,1/2)

The midpoint of AY and midpoint ZX are the same, so the given quadrilateral is a parallelogram.

Subchapter links

Exercises p.499-503