Download File

Lesson: 6.5 Squares & Rhombi
Objectives:
To Identify the PROPERTIES of SQUARES and RHOMBI
 To use the Squares and Rhombi Properties to SOLVE
Problems
GEOMETRY 6.5
A RHOMBUS is:
GEOMETRY 6.5
A RHOMBUS is:
A QUADRILATERAL
GEOMETRY 6.5
A RHOMBUS is:
A QUADRILATERAL
A PARALLELOGRAM
GEOMETRY 6.5
A RHOMBUS is:
A QUADRILATERAL
A PARALLELOGRAM
with 4 CONGRUENT SIDES
GEOMETRY 6.5
A RHOMBUS is:
A QUADRILATERAL
A PARALLELOGRAM
with 4 CONGRUENT SIDES
GEOMETRY 6.5
PROPERTIES of a Rhombus:
 Same as a Parallelogram





Opposite Sides are Parallel
Opposite Sides are Congruent
Opposite Angles are Congruent
Consecutive Sides are Supplementary
Diagonals BISECT each other.
GEOMETRY 6.5
PROPERTIES of a Rhombus:
 Same as a Parallelogram





Opposite Sides are Parallel
Opposite Sides are Congruent
Opposite Angles are Congruent
Consecutive Sides are Supplementary
Diagonals BISECT each other.
 All SIDES are CONGRUENT
GEOMETRY 6.5
PROPERTIES of a Rhombus:
 Same as a Parallelogram





Opposite Sides are Parallel
Opposite Sides are Congruent
Opposite Angles are Congruent
Consecutive Sides are Supplementary
Diagonals BISECT each other.
 All SIDES are CONGRUENT
 DIAGONALS are
GEOMETRY 6.5
PROPERTIES of a Rhombus:
 Same as a Parallelogram





Opposite Sides are Parallel
Opposite Sides are Congruent
Opposite Angles are Congruent
Consecutive Sides are Supplementary
Diagonals BISECT each other.
 All SIDES are CONGRUENT
 DIAGONALS are
 DIAGONALS
GEOMETRY 6.5
GIVEN:
ABCD is a RHOMBUS
PROOF
A
6
5
B
34
1
PROVE:
Each DIAGONAL Bisects
a PAIR of OPPOSITE ANGLES
 DIAGONALS
D
2
8
9
C
GEOMETRY 6.5
BCDE is a Rhombus
B
C
m 1  2x  20
m 2  5x  4
1
2
3
F
Find X
E
D
GEOMETRY 6.5
BCDE is a Rhombus
B
C
m 1  2x  20
m 2  5x  4
1
2
3
F
Find X
E
D
GEOMETRY 6.5
BCDE is a Rhombus
B
C
BD  15
1
2
3
F
Find BF
E
D
GEOMETRY 6.5
BCDE is a Rhombus
B
C
1
m 3  x  26
2
2
3
F
Find X
E
D
A SQUARE is BOTH
a RECTANGLE
and
a RHOMBUS
GEOMETRY 6.5
PROPERTIES of a Square:
 Same as a Parallelogram
 Opposite Sides are Parallel
 Opposite Sides are Congruent
 Opposite Angles are Congruent
 Consecutive Sides are Supplementary
 Diagonals BISECT each other.
GEOMETRY 6.5
PROPERTIES of a Square:
 Same as a Parallelogram
 Opposite Sides are Parallel
 Opposite Sides are Congruent
 Opposite Angles are Congruent
 Consecutive Sides are Supplementary
 Diagonals BISECT each other.
 Same as a Rectangle
 All ANGLES are CONGRUENT
 Diagonals are CONGRUENT
GEOMETRY 6.5
PROPERTIES of a Square:
 Same as a Parallelogram
 Opposite Sides are Parallel
 Opposite Sides are Congruent
 Opposite Angles are Congruent
 Consecutive Sides are Supplementary
 Diagonals BISECT each other.
 Same as a Rectangle
 All ANGLES are CONGRUENT
 Diagonals are CONGRUENT
 Same as a Rhombus
 All SIDES are CONGRUENT
 DIAGONALS are PERPENDICULAR
 DIAGONALS Bisect Opposite Angles
GEOMETRY 6.5
If the DIAGONALS of a PARALLELOGRAM
are CONGRUENT,
then the Parallelogram is a RECTANGLE.
GEOMETRY 6.5
If the DIAGONALS of a PARALLELOGRAM
are CONGRUENT,
then the Parallelogram is a RECTANGLE.
If the DIAGONALS of a PARALLELOGRAM
are PERPENDICULAR,
then the Parallelogram is a RHOMBUS.
GEOMETRY 6.5
If the DIAGONALS of a PARALLELOGRAM
are CONGRUENT,
then the Parallelogram is a RECTANGLE.
If the DIAGONALS of a PARALLELOGRAM
are PERPENDICULAR,
then the Parallelogram is a RHOMBUS.
If the DIAGONALS of a PARALLELOGRAM
are CONGRUENT and PERPENDICULAR,
then the Parallelogram is a
Enter YES for each PROPERTY that is TRUE
Property
Diagonals BISECT
each other
Diagonals are
CONGRUENT
Each Diagonal
BISECTS opposite
Angles
Diagonals are
PERPENDICULAR
P’gram Rectangle Rhombus Square
GEOMETRY 6.5
IF m RST  67
find m RSW
S
T
W
R
V
GEOMETRY 6.5
IF m STV  135
find m SVT
S
T
W
R
V
GEOMETRY 6.5
IF m SWT  2x  8
find x
S
T
W
R
V
GEOMETRY 6.5
IF m WRV  5x  5
m WRS  7x  19
Find x
S
T
W
R
V
All Rectangles, Rhombuses & Squares are
________________________.
All Rectangles, Rhombuses & Squares are
PARALLELOGRAMS.
All Rectangles, Rhombuses & Squares are
PARALLELOGRAMS.
All Squares are ________________________.
All Rectangles, Rhombuses & Squares are
PARALLELOGRAMS.
All Squares are RECTANGLES.
All Rectangles, Rhombuses & Squares are
PARALLELOGRAMS.
All Squares are RECTANGLES.
All Squares are ________________________.
All Rectangles, Rhombuses & Squares are
PARALLELOGRAMS.
All Squares are RECTANGLES.
All Squares are RHOMBUSES.
GEOMETRY 6.5
TRUE or FALSE
All Squares are Rhombuses.
All Rhombuses are Rectangles.
Some Rhombuses are Rectangles.
Some Parallelograms are Squares.
GEOMETRY 6.5
TRUE or FALSE
Some Parallelograms are Rectangles.
No Rectangles are Squares.
All Squares are Rectangles.
All Rhombuses are Parallelograms.
GEOMETRY 6.5
All Rectangles are Squares.
Some Rhombuses are Squares.
TRUE or FALSE
GEOMETRY 6.5
Condition
All Sides are
Rectangle

4 Right Angles

Diagonals

Diagonals
Diagonals
Bisects Angles
Rhombus
Square
GEOMETRY 6.5
THEOREM -A Parallelogram with CONGRUENT DIAGONALS
is a RECTANGLE.
GEOMETRY 6.5
THEOREM -A Parallelogram with a DIAGONAL that
BISECTS OPPOSITE ANGLES
is a RHOMBUS.
GEOMETRY 6.5
Is this PARALLELOGRAM a
Rectangle, Rhombus, Square, or NONE?
GEOMETRY 6.5
Is this PARALLELOGRAM a
Rectangle, Rhombus, Square, or NONE?
GEOMETRY 6.5
Is this PARALLELOGRAM a
Rectangle, Rhombus, Square, or NONE?
GEOMETRY 6.5
Is this PARALLELOGRAM a
Rectangle, Rhombus, Square, or NONE?
GEOMETRY 6.5
Is this PARALLELOGRAM a
Rectangle, Rhombus, Square, or NONE?
GEOMETRY 6.5
Is this PARALLELOGRAM a
Rectangle, Rhombus, Square, or NONE?
Determine whether parallelogram ABCD is a rhombus, a
rectangle, or a square for A(–2, –1),
B(–1, 3), C(3, 2), and D(2, –2). List all that apply. Explain.
GEOMETRY 6.5
You should be able to:
 Name PROPERTIES that Identify a RECTANGLE
 Name PROPERTIES that Identify a SQUARE
 Name PROPERTIES that Identify a RHOMBUS
 Use PROPERTIES to CLASSIFY a QUADRILATERAL
 Use PROPERTIES to PROVE a Figure is a
Rectangle, Square or Rhombus
 Use Properties to SOLVE Calculation Problems
GEOMETRY 6.5
GEOMETRY 6.5
GEOMETRY 6.5