1. 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

2. Answer to homework: classify the quadrilateral

3. Problem 2 HW

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

5. 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

6. 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.

7. 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

8. 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

9. 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)