1. G-05 “I can use coordinates to prove and apply properties of parallelograms.” Parallelogram, rectangle, rhombus and squares

2. Distance Formula Formula: Find the distance b/w the 2 given points. 1. A(4, -3) and B(-7, 2)

3. Distance Formula Formula: Find the distance b/w the 2 given points. 2. A(-8, 4) and B(0, -2)

4. Distance Formula Formula: Find the distance b/w the 2 given points. 3. A(11, 5) and B(-1, -2)

5. Slope Formula Formula: Find the slope of 2 given points. 1. A(-1, -4) and B(4, -8)

6. Slope Formula Formula: Find the slope of 2 given points. 2. A(7, -1) and B(6, -11)

7. Slope Formula Formula: Find the slope of 2 given points. 3. A(0, -3) and B(-9, 12)

8. Remember Regular parallelogram: 1.Opposite sides are parallel 2.Opposite sides are congruent 3.One pair of sides are parallel and congruent. When you are working with coordinates, always graph the points first.

9. Ex1a: Three vertices of parallelogram JKLM are J(3, –8), K(–2, 2), and L(2, 6). Find the coordinates of vertex M.

10. Ex 1b: Three vertices of PQSR are P(–3, –2), Q(–1, 4), and S(5, 0). Find the coordinates of vertex R.

11. 1c. Three vertices of parallelogram EFGH are E(-4, -1), F(–3, 2), and H(2, -3). Find the coordinates of vertex G

12. Ex 2: JKLM is a parallelogram. J(–1, –6), K(–4, –1), L(4, 5), M(7, 0). Prove that opposite sides are parallel. (parallel lines have SAME Slope)

13. Ex 3: ABCD is a parallelogram. A(2, 3), B(6, 2), C(5,0), D(1, 1). Prove that 1 pair of opposite sides are parallel and congruent.

14. Ex 3 cont: ABCD is a parallelogram. A(2, 3), B(6, 2), C(5, 0), D(1, 1). Prove that 1 pair of opposite sides are parallel and congruent.

15. A square is a quadrilateral with four right angles and four congruent sides. In the exercises, you will show that a square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

16. Rectangle, Rhombus, or Square? 1.Diagonals are congruent. (rectangle) 2.Diagonals are perpendicular. (rhombus) both 3.Diagonals are both congruent and perpendicular. (rectangle, rhombus, square)

17. Example 4a Determine if the quadrilateral is a rectangle, rhombus, and/or square. Give all the names that apply. Given: AD is 25 and BC is 14 Slope for AD is 4/5 and BC is -5/4

18. Example 4b Determine if the quadrilateral is a rectangle, rhombus, and/or square. Give all the names that apply. Given: AD is 6 and BC is 6 Slope for AD is 2/3 and BC is -2

19. Example 4c Determine if the quadrilateral is a rectangle, rhombus, and/or square. Give all the names that apply. Given: AD is 18.2 and BC is 18.2 Slope for AD is 1/4 and BC is -4

20. Example 4d Determine if the quadrilateral is a rectangle, rhombus, and/or square. Give all the names that apply. Given: AD is and BC is Slope for AD is 1 and BC is -1

21. Ex 5a: Use the diagonals to determine whether a parallelogram w/the given vertices is a rectangle, rhombus, or square. Give all the names that apply. A(0, 2) B(3, 6) C(8, 6) D(5, 2) [1] Graph Note: if a quadrilateral is Both a rectangle and rhombus, then it is a square.

22. A(0, 2) B(3, 6) C(8, 6) D(5, 2) [2] Determine if ABCD is a rectangle (diagonals are congruent)

23. A(0, 2) B(3, 6) C(8, 6) D(5, 2) [3] Determine if ABCD is a rhombus (diagonals are perpendicular; slope is opposite reciprocal)

24. Ex 5b: Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square. Give all the names that apply. P(–1, 4), Q(2, 6), R(4, 3), S(1, 1)

25. [2] Determine if PQRS is a rectangle (diagonals are congruent)

26. P(–1, 4), Q(2, 6), R(4, 3), S(1, 1) [3] Determine if PQRS is a rhombus (diagonals are perpendicular; slope is opposite reciprocal)