Transcript Document
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 1 2 3 m 2 5 x 4 F Find X E D GEOMETRY 6.5 BCDE is a Rhombus B C m 1 2x 20 1 2 3 m 2 5 x 4 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 S T find m RSW W R V GEOMETRY 6.5 IF m STV 135 S T find m SVT W R V GEOMETRY 6.5 IF m SWT 2x 8 S T find x W R V GEOMETRY 6.5 IF m WRV 5x 5 S T m WRS 7x 19 Find x 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