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Section 5-4

Section 5-4. Special Parallelograms. RECTANGLE. A rectangle is a quadrilateral with four right angles. Therefore, every rectangle is a parallelogram. Rectangle. Why?. D. C. A. B. Both pairs of opposite angles are congruent. Rhombus.

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Section 5-4

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  1. Section 5-4 Special Parallelograms

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

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

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

  11. 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 AngleAis 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? Always • 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

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