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. Warm-up Copy and complete the table below by placing a yes (to mean always) or a no (to mean not always) in each empty space. parallelogram rectangle square Opposite sides are ∣∣ Opposite sides are ≅ Opposite angles are ≅ Diagonals bisect each other Diagonals are⊥ Diagonals are ≅ rhombus kite Yes Yes Yes Yes no Yes no Yes Yes Yes Yes Yes Yes no Yes Yes no Yes Yes Yes no no Yes Yes Yes no no no Yes Yes

Answer to homework: classify the quadrilateral

Problem 2 HW

Find the coordinates of point A in parallelogram PRAM M(b, c) Find the coordinates of point A in parallelogram PRAM (a + b, c)

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

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

B(1, 5) O(9, 9) X(11, 5) Y(3, 1) Is BOXY a rectangle? Why? The diagonals of BOXY are __________________ BOXY is a rectangle because its adjacent sides are perpendicular. The diagonals are congruent. 10

More Practice!!! 7 75 16 A B C D x + 9 2x - 7 Perimeter ABCD = 46 Find the measure of 1. 2. A B C D 63 4x +3 Perimeter ABCD = 16x – 12. Measure of AD =_____________ 7 75 16

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