1. Special Parallelograms
Section 5-4
Special
Parallelograms

2. RECTANGLE
A rectangle is a quadrilateral with four right angles. Therefore, every rectangle is a parallelogram.

3. Both pairs of opposite angles are congruent.
Rectangle
Why? D C A B
Both pairs of opposite angles are congruent.

4. Rhombus
A rhombus is a quadrilateral with four congruent sides. Therefore, every rhombus is a parallelogram.

5. Both pairs of opposite sides are congruent.
rhombus
Why? D A C B
Both pairs of opposite sides are congruent.

6. Square
A square is a quadrilateral with four right angles and four congruent sides. Therefore, every square is a rectangle, a rhombus, and a parallelogram.

7. Both pairs of opposite angles (and sides) are congruent.
Square
Why? D C A B
Both pairs of opposite angles (and sides) are congruent.

8. Conclusion: Since rectangles, rhombuses and squares are all parallelograms, they have all the properties of a parallelogram.

9. The diagonals of a rectangle are congruent.
Theorem 5-12
The diagonals of a rectangle are congruent. D C A B

10. The diagonals of a rhombus are perpendicular.
Theorem 5-13
The diagonals of a rhombus are perpendicular. D A C B

11. Each diagonal of a rhombus bisects two angles of the rhombus.
Theorem 5-14
Each diagonal of a rhombus bisects two angles of the rhombus. D A C B

12. Theorem 5-15
The midpoint of the hypotenuse of a right triangle is equidistant from the vertices. A D C B

13. Theorem 5-16
If an angle of a parallelogram is a right angle, then the parallelogram is a rectangle. D C
Angle A is a Rt. Angle
Thus,
ABCD is a Rectangle! A B

14. Theorem 5-17
If two consecutive sides of a parallelogram are congruent, then the parallelogram is a rhombus.

15. Theorem 5-17
Thus, ABCD is a Rhombus D A C B

16. Always, Sometimes or Never?
A square is _________ a rhombus?
The diagonals of a parallelogram ____________bisect the angles of the parallelogram?
A quadrilateral with one pair of sides congruent and one pair parallel is ___________ a parallelogram?
Sometimes
Sometimes

17. Always, Sometimes or Never?
The diagonals of a rhombus are ___________ congruent?
A rectangle __________ has consecutive sides congruent?
A rectangle __________ has perpendicular diagonals?
Sometimes
Sometimes
Sometimes

18. Always, Sometimes or Never?
The diagonals of a rhombus ___________ bisect each other?
The diagonals of a parallelogram are __________ perpendicular bisectors of each other?
Always
Sometimes