body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Tests for Parallelograms

Finish the assignment

Continue to next subchapter

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