1. HONORS GEOMETRY 6.3: Test for Parallelograms Day Two

2. Do Now: Complete the Do Now given to you when you entered class today

3. Homework Questions? Comments? Confusions? Concerns? ASK ASK ASK!

4. Today: Let’s move everything into the coordinate plane!

5. Example One: Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices F(-2, 4), G(3,5), H(2, -3) and J(-3, -4)

6. Recall:

7. Example One (Again!) Determine the coordinates of the intersection of the diagonals of parallelogram FGHJ with vertices F(-2, 4), G(3,5), H(2, -3) and J(-3, -4)

8. Example Two: Determine the coordinates of the intersection of the diagonals of parallelogram RSTU with vertices R(-8, -2), S(-6, 7), T(6, 7) and U(4, -2).

9. You Try! Determine the coordinates of the intersection of the diagonals of parallelogram MNPR with vertices M(-3,0), N(-1, 3), P(5, 4) and R(3,1).

10. Different Way to Ask It: Example Three: Graph quadrilateral FGHJ with F(-5, 4), G(3, 3), H(1, -3), J(-7, -3). Determine whether the quadrilateral is a parallelogram using the midpoint formula.

11. You Try! Graph quadrilateral QRST with Q(2, -4), R(4, 3), S(-3, 6), and T(-5, -1). Determine whether the quadrilateral is a parallelogram using the midpoint formula.

12. Example Four: Graph Quadrilateral KLMN with vertices K(2, 3), L(8,4), M(7, -2) and N(1, -3). Determine whether the quadrilateral is a parallelogram using the slope formula.

13. Recall: Parallelograms are quadrilaterals that have PARALLEL opposite sides….. Parallel lines have slopes that are __________________

14. Slope Formula:

15. Example Four (Again!) Graph Quadrilateral KLMN with vertices K(2, 3), L(8,4), M(7, -2) and N(1, -3). Determine whether the quadrilateral is a parallelogram using the slope formula.

16. Example Five: Graph Quadrilateral FGHJ with vertices F(-2, 4), G(4, 2), H(4, -2) and J(-2, -1). Determine whether the quadrilateral is a parallelogram using the slope formula.

17. You Try!: Graph Quadrilateral QSTR with vertices Q(-1, 3), R(3, 1), S(2, -3) and T(-2, -1). Determine whether the quadrilateral is a parallelogram using the slope formula.

18. Example Six: Graph quadrilateral ABCD with A(3, 3), B(8, 2), C(6, -1), D(1, 0). Determine whether the quadrilateral is a parallelogram using the distance formula.

19. Recall: In a parallelogram– OPPOSITE SIDES ARE CONGRUENT. I.E. they have the same distance!

20. Distance Formula:

21. Example Six (Again!) Graph quadrilateral ABCD with A(3, 3), B(8, 2), C(6, -1), D(1, 0). Determine whether the quadrilateral is a parallelogram using the distance formula.

22. You Try!: Graph quadrilateral WXYZ with W(-2, 4), X(5,4), Y(8, -1) and Z(-1, -1). Determine whether the quadrilateral is a parallelogram using the distance formula.

23. Practice Problems Try some on your own/in small groups As always, don’t hesitate to ask me questions if you are confused!

24. Exit Ticket: Determine using any method whether quadrilateral QRST is a parallelogram is Q(3, 5), R(1, -2), S(-6, 2), T(-4, 7)