Lesson: Objectives: 6.5 Squares & Rhombi  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 DIAGONALS PROOF A B C D GIVEN: ABCD is a RHOMBUS PROVE: Each DIAGONAL Bisects a PAIR of OPPOSITE ANGLES

GEOMETRY 6.5 B C D E F BCDE is a Rhombus Find X

GEOMETRY 6.5 B C D E F BCDE is a Rhombus Find X

GEOMETRY 6.5 B C D E F BCDE is a Rhombus Find BF

GEOMETRY 6.5 B C D E F BCDE is a Rhombus Find X

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  Diagonals are CONGRUENT  All ANGLES 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.  All SIDES are CONGRUENT  DIAGONALS are PERPENDICULAR  DIAGONALS Bisect Opposite Angles Same as a Rectangle  Diagonals are CONGRUENT Same as a Rhombus  All ANGLES are CONGRUENT

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

PropertyP’gramRectangleRhombusSquare Diagonals BISECT each other Diagonals are CONGRUENT Each Diagonal BISECTS opposite Angles Diagonals are PERPENDICULAR Enter YES for each PROPERTY that is TRUE

GEOMETRY 6.5 S T V R W

S T V R W

S T V R W

S T V R W

All Rectangles, Rhombuses & Squares are ________________________.

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 ________________________. All Squares are RECTANGLES. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

All Squares are RHOMBUSES. All Squares are RECTANGLES. All Rectangles, Rhombuses & Squares are PARALLELOGRAMS.

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 Some Parallelograms are Rectangles. No Rectangles are Squares. All Squares are Rectangles. All Rhombuses are Parallelograms. TRUE or FALSE

GEOMETRY 6.5 TRUE or FALSE All Rectangles are Squares. Some Rhombuses are Squares.

GEOMETRY 6.5 ConditionRectangleRhombusSquare All Sides are 4 Right Angles Diagonals Bisects Angles

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