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Exploring Rhombi and Squares in Geometry

Learn about the properties of rhombi and squares, how to recognize them, and apply their characteristics in geometry. Understand the distinctions between parallelograms, rhombuses, and squares with practical examples and comparisons.

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Exploring Rhombi and Squares in Geometry

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  1. 6-5 Rhombi and SquaresN#____ ____/____/____ SLG : Students will be able to recognize and apply the properties of rhombi and squares. They will also be able to determine if a parallelogram is a rhombus or square.

  2. A parallelogram with all four congruent sides R H Rhombus: Every rhombus has all of the properties of parallelograms; opposite sides parallel, opposite sides congruent, opposite angles congruent, consecutive angles supplementary, diagonals bisect each other. M O

  3. Properties of a Rhombus: • Opposite sides parallel. • Opposite sides congruent • Opposite angles congruent. • Consecutive angles supplementary. • Diagonals bisect each other. Parallelogram All four sides are congruent Rhombus Diagonals are perpendicular Diagonals are angle bisectors

  4. A parallelogram with all four congruent sides and four right angles S Q Square: Since a square has 4 right angles, a square is a rectangle. Since a square has 4 congruent sides, a square is a rhombus. A U

  5. Properties of a square: • Opposite sides parallel. • Opposite sides congruent. • Opposite angles congruent. • Consecutive angles supplementary. • Diagonals bisect each other. Parallelogram All four angles are right angles Rectangle Diagonals are congruent All four sides are congruent Diagonals are perpendicular Rhombus Diagonals are angle bisectors

  6. Quadrilaterals Parallelograms Rectangles Squares Rhombi

  7. G F Quadrilateral FGHJ is a rhombus. Find each value or measure. E1 E2 K H J

  8. E3 Determine whether quadrilateral ABCD is a parallelogram, rectangle, rhombus, and or square? A(-2, -1), B(-1, 3), C(3, 2), D(2, -2) Compare the slopes: Compare the diagonal slopes: Parallelogram!! SQUARE!!!

  9. Compare the side distances: E3 Determine whether quadrilateral ABCD is a parallelogram, rectangle, rhombus, and or square? A(-2, -1), B(-1, 3), C(3, 2), D(2, -2) Compare the diagonal distances: Rhombus!!! SQUARE!!!

  10. A#____ ____/____/____ PWS 6-5 & SWS 6-5

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