1. Properties of Rhombuses, Rectangles, and Squares

2. Properties of Rhombuses, Rectangles, and Squares
A rhombus is a parallelogram with
four congruent sides.

3. Properties of Rhombuses, Rectangles, and Squares
A rectangle is a parallelogram with
four right angles.

4. Properties of Rhombuses, Rectangles, and Squares
A square is a parallelogram with
four congruent sides and four right angles.

5. Section 6.4 – Properties of Rhombuses, Rectangles, and Squares

6. Properties of Rhombuses, Rectangles, and Squares
Problem 1:
Is Parallelogram ABCD a rhombus, rectangle or square? Explain!

7. Properties of Rhombuses, Rectangles, and Squares
Problem 1b:
Is Parallelogram EFGH a rhombus, rectangle or square? Explain!

8. Properties of Rhombuses, Rectangles, and Squares

9. Properties of Rhombuses, Rectangles, and Squares

10. Properties of Rhombuses, Rectangles, and Squares
Problem 2:
What are the measures of the numbered angles in rhombus ABCD?

11. Properties of Rhombuses, Rectangles, and Squares
Problem 2:
What are the measures of the numbered angles in rhombus PQRS?

12. Properties of Rhombuses, Rectangles, and Squares
Problem 2:
What are the measures of the numbered angles in the rhombus?

13. Properties of Rhombuses, Rectangles, and Squares
Problem 2:
What are the measures of the numbered angles in the rhombus?

14. Properties of Rhombuses, Rectangles, and Squares

15. Properties of Rhombuses, Rectangles, and Squares
Problem 3:
In rectangle RSBF, SF = 2x + 15 and
RB = 5x – 12. What is the length of a diagonal?

16. Properties of Rhombuses, Rectangles, and Squares
Problem 4:
LMNP is a rectangle. Find the value of x and the length of each diagonal
LN = 5x – 8 and MP = 2x + 1

17. Properties of Rhombuses, Rectangles, and Squares
Problem 5:
Determine the most precise name for each quadrilateral.

18. Properties of Rhombuses, Rectangles, and Squares
Problem 6:
List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square.
Opposite angles are congruent.

19. Properties of Rhombuses, Rectangles, and Squares
Problem 6b:
List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square.
Diagonals are congruent

20. Properties of Rhombuses, Rectangles, and Squares
Problem 6c:
List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square.
Each diagonal bisects opposite angles

21. Properties of Rhombuses, Rectangles, and Squares
Problem 6d:
List all quadrilaterals that have the given property. Chose among parallelogram, rhombus, rectangle, or square.
Opposite sides are parallel

22. Properties of Rhombuses, Rectangles, and Squares

23. Properties of Rhombuses, Rectangles, and Squares

24. Conditions for Rhombuses, Rectangles, and Squares

25. Conditions for Rhombuses, Rectangles, and Squares

26. Conditions for Rhombuses, Rectangles, and Squares

27. Conditions for Rhombuses, Rectangles, and Squares

28. Conditions for Rhombuses, Rectangles, and Squares
Problem 1:
Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

29. Conditions for Rhombuses, Rectangles, and Squares
Problem 1b:
Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

30. Conditions for Rhombuses, Rectangles, and Squares
Problem 1c:
Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

31. Conditions for Rhombuses, Rectangles, and Squares
Problem 1d:
Can you conclude that the parallelogram is a rhombus, a rectangle, or a square? Explain!

32. Conditions for Rhombuses, Rectangles, and Squares
Problem 2:
For what value of x is parallelogram ABCD a rhombus?

33. Conditions for Rhombuses, Rectangles, and Squares
Problem 2b:
For what value of x is the parallelogram a rectangle?

34. Conditions for Rhombuses, Rectangles, and Squares
Problem 2c:
For what value of x is the parallelogram a rhombus?

35. Conditions for Rhombuses, Rectangles, and Squares
Problem 2d:
For what value of x is the parallelogram a rectangle?

36. Conditions for Rhombuses, Rectangles, and Squares
Problem 2e:
For what value of x is the parallelogram a rectangle?

37. Conditions for Rhombuses, Rectangles, and Squares
Problem 3:
Builders use properties of diagonals to “square up” rectangular shapes like building frames and playing-field boundaries. Suppose you are on the volunteer building team at the right. You are helping to lay out a rectangular patio for a youth center. How can you use the properties of diagonals to locate the four corners?

38. Conditions for Rhombuses, Rectangles, and Squares
Problem 4:
Determine whether the quadrilateral can be a parallelogram. Explain!
The diagonals are congruent, but the quadrilateral has no right angles.

39. Conditions for Rhombuses, Rectangles, and Squares
Problem 4b:
Determine whether the quadrilateral can be a parallelogram. Explain!
Each diagonal is 3 cm long and two opposite sides are 2 cm long.

40. Conditions for Rhombuses, Rectangles, and Squares
Problem 4c:
Determine whether the quadrilateral can be a parallelogram. Explain!
Two opposite angles are right angles but the quadrilateral is not a rectangle.

41. Conditions for Rhombuses, Rectangles, and Squares

42. Conditions for Rhombuses, Rectangles, and Squares