Special Parallelograms Section 5-4 Special Parallelograms

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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