1. Lesson: Objectives: 6.5 Squares & Rhombi  To Identify the PROPERTIES of SQUARES and RHOMBI  To use the Squares and Rhombi Properties to SOLVE Problems

2. GEOMETRY 6.5 A RHOMBUS is:

3. GEOMETRY 6.5 A RHOMBUS is: A QUADRILATERAL

4. GEOMETRY 6.5 A RHOMBUS is: A QUADRILATERAL A PARALLELOGRAM

5. GEOMETRY 6.5 A RHOMBUS is: A QUADRILATERAL A PARALLELOGRAM with 4 CONGRUENT SIDES

6. GEOMETRY 6.5 A RHOMBUS is: A QUADRILATERAL A PARALLELOGRAM with 4 CONGRUENT SIDES

7. GEOMETRY 6.5 PROPERTIES of a Rhombus: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other.

8. GEOMETRY 6.5 PROPERTIES of a Rhombus: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other. All SIDES are CONGRUENT

9. GEOMETRY 6.5 PROPERTIES of a Rhombus: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other. All SIDES are CONGRUENT DIAGONALS are

10. GEOMETRY 6.5 PROPERTIES of a Rhombus: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other. All SIDES are CONGRUENT DIAGONALS are DIAGONALS

11. GEOMETRY 6.5 DIAGONALS PROOF A B C D 5 6 3 4 8 9 2 1 GIVEN: ABCD is a RHOMBUS PROVE: Each DIAGONAL Bisects a PAIR of OPPOSITE ANGLES

12. GEOMETRY 6.5 B C D E F 1 2 3 BCDE is a Rhombus Find X

13. GEOMETRY 6.5 B C D E F 1 2 3 BCDE is a Rhombus Find X

14. GEOMETRY 6.5 B C D E F 1 2 3 BCDE is a Rhombus Find BF

15. GEOMETRY 6.5 B C D E F 1 2 3 BCDE is a Rhombus Find X

16. A SQUARE is BOTH a RECTANGLE and a RHOMBUS

17. GEOMETRY 6.5 PROPERTIES of a Square: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other.

18. GEOMETRY 6.5 PROPERTIES of a Square: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other. Same as a Rectangle  Diagonals are CONGRUENT  All ANGLES are CONGRUENT

19. GEOMETRY 6.5 PROPERTIES of a Square: Same as a Parallelogram  Opposite Sides are Parallel  Opposite Sides are Congruent  Opposite Angles are Congruent  Consecutive Sides are Supplementary  Diagonals BISECT each other.  All SIDES are CONGRUENT  DIAGONALS are PERPENDICULAR  DIAGONALS Bisect Opposite Angles Same as a Rectangle  Diagonals are CONGRUENT Same as a Rhombus  All ANGLES are CONGRUENT

20. GEOMETRY 6.5 If the DIAGONALS of a PARALLELOGRAM are CONGRUENT, then the Parallelogram is a RECTANGLE.

21. GEOMETRY 6.5 If the DIAGONALS of a PARALLELOGRAM are CONGRUENT, then the Parallelogram is a RECTANGLE. If the DIAGONALS of a PARALLELOGRAM are PERPENDICULAR, then the Parallelogram is a RHOMBUS.

22. GEOMETRY 6.5 If the DIAGONALS of a PARALLELOGRAM are CONGRUENT, then the Parallelogram is a RECTANGLE. If the DIAGONALS of a PARALLELOGRAM are PERPENDICULAR, then the Parallelogram is a RHOMBUS. If the DIAGONALS of a PARALLELOGRAM are CONGRUENT and PERPENDICULAR, then the Parallelogram is a

23. PropertyP’gramRectangleRhombusSquare Diagonals BISECT each other Diagonals are CONGRUENT Each Diagonal BISECTS opposite Angles Diagonals are PERPENDICULAR Enter YES for each PROPERTY that is TRUE

24. GEOMETRY 6.5 S T V R W

25. S T V R W

26. S T V R W

27. S T V R W

28. All Rectangles, Rhombuses & Squares are ________________________.

29. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

30. All Squares are ________________________. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

31. All Squares are RECTANGLES. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

32. All Squares are ________________________. All Squares are RECTANGLES. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

33. All Squares are RHOMBUSES. All Squares are RECTANGLES. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

34. GEOMETRY 6.5 TRUE or FALSE All Squares are Rhombuses. All Rhombuses are Rectangles. Some Rhombuses are Rectangles. Some Parallelograms are Squares.

35. GEOMETRY 6.5 Some Parallelograms are Rectangles. No Rectangles are Squares. All Squares are Rectangles. All Rhombuses are Parallelograms. TRUE or FALSE

36. GEOMETRY 6.5 TRUE or FALSE All Rectangles are Squares. Some Rhombuses are Squares.

37. GEOMETRY 6.5 ConditionRectangleRhombusSquare All Sides are 4 Right Angles Diagonals Bisects Angles

38. GEOMETRY 6.5 THEOREM -- A Parallelogram with CONGRUENT DIAGONALS is a RECTANGLE.

39. GEOMETRY 6.5 THEOREM -- A Parallelogram with a DIAGONAL that BISECTS OPPOSITE ANGLES is a RHOMBUS.

40. GEOMETRY 6.5 Is this PARALLELOGRAM a Rectangle, Rhombus, Square, or NONE?

41. GEOMETRY 6.5 Is this PARALLELOGRAM a Rectangle, Rhombus, Square, or NONE?

42. GEOMETRY 6.5 Is this PARALLELOGRAM a Rectangle, Rhombus, Square, or NONE?

43. GEOMETRY 6.5 Is this PARALLELOGRAM a Rectangle, Rhombus, Square, or NONE?

44. GEOMETRY 6.5 Is this PARALLELOGRAM a Rectangle, Rhombus, Square, or NONE?

45. GEOMETRY 6.5 Is this PARALLELOGRAM a Rectangle, Rhombus, Square, or NONE?

46. Determine whether parallelogram ABCD is a rhombus, a rectangle, or a square for A(–2, –1), B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.

47. GEOMETRY 6.5 You should be able to: Name PROPERTIES that Identify a RECTANGLE Name PROPERTIES that Identify a SQUARE Name PROPERTIES that Identify a RHOMBUS Use PROPERTIES to CLASSIFY a QUADRILATERAL Use PROPERTIES to PROVE a Figure is a Rectangle, Square or Rhombus Use Properties to SOLVE Calculation Problems

53. GEOMETRY 6.5