1. 5.2 Proving Quadrilaterals are Parallelograms Definition of Parallelogram: Both pairs of opposite sides are parallel.

2. REMEMBER Back from Chapter 3 that all the angles of a quadrilateral = 360 o.

3. 5 Ways to Prove Parallelograms 1.Show both pairs of opposite sides are parallel 2.Show both pairs of opposite sides are congruent 3.Show both pairs of opposite angles are congruent 4.Show one pair of opposite sides congruent and parallel 5.Show that the diagonals bisect each other. 95 85 95 G J K B o o o

4. Finding missing values What values of x and y make the quadrilateral a parallelogram. 3x – 41 = 2x - 6 -2x = - 2x x – 41 = -6 + 41 = + 41 x = 35 2(35) – 6 = 64 64 o 180 o – 64 o 116 o 5y + 16 = 116 o 5y = 100 o y = 20 o

5. Missing Values What values of x and y make the quadrilateral a parallelogram. 2x – y = 9 3x + 2y = 10 2(2x – y = 9)4x – 2y = 18 3x + 2y = 10 7x = 28 x = 4 3(4) + 2y = 10 12 + 2y = 10 2y = -2 y = -1

6. x2x2 Back to your Algebra 1 days Find the missing values. They are all LENGTHS! 5y = 3y + 16 -3y -3y 2y = 16 y = 8 x 2 = 2x + 8 A Quadratic Equation! Set it = 0 x 2 = 2x + 8 -2x - 8 x 2 – 2x – 8 = 0 Now FACTOR it ( )( ) = 0xx Factors of 8 That make a -2 1, 8 2, 4 2 4- + (x + 2)(x – 4) = 0 x + 2 = 0 x = -2 x – 4 = 0 x = 4

7. x2x2 Back to your Algebra 1 days Find the missing values. They are all LENGTHS! 5y = 3y + 16 -3y -3y 2y = 16 y = 8 x = -2 x = 4 x 2 = 2x + 8 (-2) 2 = 2(-2) + 8 4 = -4 + 8 4 = 4 x = -2 is Good x 2 = 2x + 8 (4) 2 = 2(4) + 8 16 = 8 + 8 16 = 16 x = 4 is Good

8. PRACTICE Page 173 Classroom Exercises #1 – 10 DRAW DIAGRAMS!