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Special Parallelograms
Lesson 5.4
Geometry Honors
Page 184
Objectives
Apply the definitions and identify the special properties of a
rectangle, a rhombus, and a square.
Determine when a parallelogram is a rectangle, rhombus, or
square.
Rectangle
A parallelogram with four right angles.
Both pairs of opposite angles are congruent.
Every rectangle is a parallelogram.
Rhombus
A quadrilateral with four congruent sides.
Both pairs of opposite sides are congruent.
Every rhombus is a parallelogram.
Square
A quadrilateral with four right angles and four congruent sides.
Both pairs of opposite angles and opposite sides are congruent.
A square is also a rectangle, a rhombus, and a parallelogram.
Theorem 5-12
The diagonals of a rectangle are congruent.
Theorem 5-13
The diagonals of a rhombus are perpendicular.
Theorem 5-14
Each diagonal of a rhombus bisects two angles of the
rhombus.
Theorem 5-15
The midpoint of the hypotenuse of a right angle is equidistant
from the three vertices.
Theorem 5-16
If an angle of a parallelogram is a right angle, then the
parallelogram is a rectangle.
Theorem 5-17
If two consecutive sides of a parallelogram are congruent,
then the parallelogram is a rhombus.
The Family of Quadrilaterals
Practice
Reply with always, sometimes, or never.
1.
2.
3.
4.
5.
6.
7.
8.
A square it a rhombus.
The diagonals of a parallelogram bisect the angles of the
parallelogram.
A quadrilateral with one pair of sides congruent is a
parallelogram.
The diagonals of a rhombus are congruent.
A rectangle has consecutive sides congruent.
A rectangle has perpendicular diagonals.
The diagonals of a rhombus bisect each other.
The diagonals of a parallelogram are perpendicular bisectors
of each other.
Homework
Page 187 - 189
Problems
1 - 10, 14, 17, 28, 30, 32, 33, 34,
36, 37, 40 - 42