1. COORDINATE GEOMETRY PROOFS USE OF FORMULAS TO PROVE STATEMENTS ARE TRUE/NOT TRUE: Distance: d= Midpoint: midpoint= ( ) Slope: m =

2. Distance Formula Distance: d= When two line segments have the same distance, they are equal in length.

3. Midpoint Formula Midpoint = When two line segments have the same midpoint, it shows that they are bisecting each other.

4. Slope Formula Slope: m = When two lines have equal slopes, they are parallel. When two lines have slopes which are negative reciprocals, they are perpendicular.

5. Proving a Quadrilateral is a Parallelogram Methods: 1.Show that both pairs of opposite sides are equal. Use distance formula for 4 sides 2.Show that both pairs of opposite sides are parallel. Use slope formula for 4 sides 3.Show that diagonals bisect each other. Use midpoint formula for 2 diagonals 4.Show one pair of opposite sides equal and parallel Use distance and slope for 2 opposite sides

6. Write a conclusion statement: 1.The quadrilateral is a parallelogram since both pairs of opposite sides of the quadrilateral are equal. 2.The quadrilateral is a parallelogram since both pairs of opposite sides of the quadrilateral are parallel because their slopes are equal.

7. 3.The quadrilateral is a parallelogram since the diagonals bisect each other because they have the same midpoint. 4.The quadrilateral is a parallelogram since it has one pair of opposite sides which are equal and parallel because they have the same slope.

8. Examples 1.Prove that quadrilateral ABCD is a parallelogram if the coordinates of A( 2, 3 ), B(8,4 ), C(7, -6 ), and D(1, -7 ) 2.Prove quadrilateral JKLM is a parallelogram if the coordinates are: J (0,0), K(a,0), L(a+b,c), and M(b,c).

9. Homework: Prove each of the following quadrilaterals are parallelograms. Be sure to use each method which corresponds to the question number. 1.A ( -3,-2 ) B ( 2,-2) C ( 4,1 ) D ( -1,1 ) 2.P ( 4,9 ) Q( 6,12) R ( 5,8) S ( 3,5) 3.J ( 1,-3) K ( 1,4) L ( 6,8 ) M ( 6,1) 4.M ( -7,5 ) A ( 2,5 ) T ( 6,-4 ) H ( -3,-4)