1. Review for Parallelogram Properties Quiz G.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle.

2. Warm-up Show that A(2, -1), B(1, 3), C(6, 5), and D(7, 1) are the vertices of a parallelogram.

3. Method 1 Show that opposite sides have the same slope, so they are parallel.

4. Method 2 Show that opposite sides have the same length.

5. Method 3

6. Sometimes, Always or Never True  The diagonals of a parallelogram are congruent.  The consecutive angles of a rectangle are congruent and supplementary.  The diagonals of a rectangle bisect each other.  The diagonals of a rectangle bisect the angles.  The diagonals of a square are perpendicular bisectors of each other.  A square is a rectangle. Sometimes, if it’s a rectangle. Always Sometimes, if it’s a square. Always

7. Sometimes, Always or Never True  A diagonal divides a square into two isosceles right triangles.  Consecutive angles in a parallelogram are congruent Always Sometimes, if it’s a square or a rectangle. Consecutive angles are always supplementary.

8. B(1, 5) O(9, 9) X(11, 5) Y(3, 1) Is BOXY a rectangle? Why? The diagonals of BOXY are __________________

9. More Practice!!! AB CD x + 9 2x - 7 Perimeter ABCD = 46 Find the measure of 1. 2. AB CD 63 4x +3 Perimeter ABCD = 16x – 12. Measure of AD =_____________ 16775

10. READY FOR A CHALLENGE??? P R(a, 0) A(b, c)M(?, ?) Find the coordinates of point M in parallelogram PRAM (b-a, c)