#### Transcript Rhombi And Squares

```Rhombi And Squares
Chapter 6 Section 5
Rhombus
A rhombus is a parallelogram with four
congruent sides
Properties of a
Rhombus
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
Plus, Diagonals are Perpendicular
And, Diagonals bisect each pair of opposite angles
Square
A square is a parallelogram with four congruent
sides and four right angles.
Since a square is a parallelogram with four
congruent sides, a square is also a Rhombus
Since a square is a parallelogram with four right
angles, a square is also a rectangle.
Properties of a Square
Opposite sides are congruent (duh)
Opposite angles are congruent (duh)
Consecutive angles are supplementary
Diagonals bisect each other
Plus, diagonals are congruent (since a square is a
rectangle)
Plus, diagonals are perpendicular (since a square is a
rhombus)
And, diagonals bisect each pair of opposite angles
(rhombus)
Diagonals of a
Rhombus
Example
We know that the diagonals of a rhombus bisects the two angles of the
rhombus and that the diagonals are perpendicular, so find the measures
of the numbered angles in each of the following:
Something to think
SO, A SQUARE HAS ALL THE PROPERTIES OF A
RECTANGLE AND A RHOMBUS
IN ORDER TO BE A RECTANGLE, THE ONLY
STIPULATION IS A
PARALLELOGRAM WITH 4 RIGHT ANGLES.
DO YOU THINK A SQUARE IS ALWAYS A RECTANGLE?
IN ORDER TO BE A SQUARE IT MUST HAVE FOUR RIGHT ANGLES AND
FOUR CONGRUENT SIDES!!
IS A RECTANGLE ALWAYS A SQUARE?
IN ORDER TO BE A RHOMBUS, THE ONLY
STIPULATION IS A PARALLELOGRAM
WITH FOUR CONGRUENT SIDES.
DO YOU THINK A SQUARE IS ALWAYS A RHOMBUS?
IN ORDER TO BE A SQUARE, THE FIGURE MUST HAVE
4 CONGRUENT SIDES
AND FOUR RIGHT ANGLES!
IS A RHOMBUS ALWAYS A SQUARE?
What’s the most precise
name? (parallelogram, rhombus,
square, rectangle)
Find the value of the
variables...
Try this one…(from