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Special Parallelograms

In this engaging lesson, students will explore the properties of special parallelograms, including rectangles, rhombuses, and squares. Using index cards, rulers, protractors, scissors, and tape, students will construct and measure various quadrilaterals. Through hands-on activities, they will investigate the relationships between opposite sides, angles, and diagonals. By the end of the lesson, students will be able to identify and describe the characteristics of each type of parallelogram, enhancing their understanding of geometry.

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Special Parallelograms

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  1. Special Parallelograms Geometry Unit 12, Day 3 Ms. Reed

  2. For this lesson, you will need: • 2 index cards • A ruler • A protractor • Scissors • Piece of Tape

  3. Exploration • Mark a point somewhere along the bottom edge of your index card. • Draw a line from that point to the top right corner of the rectangle to form a triangle. Amy King

  4. Exploration • Cut along this line to remove the triangle. • Attach the triangle to the left side of the rectangle. • What shape have you created? Amy King

  5. opposite sides parallel opposite side congruent opposite angles are congruent diagonals bisect each other Parallelogram Properties: Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

  6. Back to your card… • Fold along CD so that it lies along AD creating line ED. • Cut along CE and discard the excess section (ABEC). • Unfold the quadrilateral. • Is this a parallelogram? E C Amy King

  7. Back to your card… • Measure the length of the 4 sides. What is the relationship of the sides? • Draw diagonal DE. • Measure FED, DEC, FDE, and CDE. What is the relationship of these angles? E F Amy King

  8. Back to your card… • Draw diagonal FC. • Measure EFC, CFD, ECF, and FCD. What is the relationship of these angles? • Measure the 4 angles formed where the diagonals intersect. What is the measure of these angles? E F Amy King

  9. opposite sides are parallel opposite sides are congruent opposite angles are congruent diagonals bisect each other diagonals bisect opposite angles diagonals are perpendicular Properties of a Rhombus has 4 congruent sides (def) Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

  10. Take out a new index card… • Is your card a parallelogram? • Why? • What is the relationship of the 4 angles of your card? • What is the name of this quadrilateral? • Measure the length of each diagonal. What conjecture can you make regarding the lengths of the diagonals of a rectangle?

  11. opposite sides parallel opposite sides congruent has congruent (right) angles (definition) diagonals bisect each other diagonals are congruent (AC = BD) Properties of a Rectangle Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

  12. Back to the index card… • Fold the corner of your card down to make a triangle. Cut off the rectangle at the bottom edge and unfold the card. • Is this quadrilateral • A parallelogram? • A rectangle? • A rhombus? http://www.kolumbus.fi/~y602648/semisuper/kuva/lentskari1.jpg

  13. Back to the index card… • Use your ruler to draw two diagonals of the quadrilateral. • Measure the angles formed by the side of the quadrilateral and the diagonal. What conjecture can you make about these angles? • What is the name of this quadrilateral? http://www.kolumbus.fi/~y602648/semisuper/kuva/lentskari1.jpg

  14. opposite sides parallel has 4 congruent sides and 4 congruent (right) angles diagonals bisect each other diagonals are congruent (AC=BD) diagonals bisect opposite angles all bisected angles equal 45º diagonals are perpendicular Properties of a Square opposite angles congruent(all right) Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

  15. Complete the Chart:

  16. Homework Work Packet: Special Parallelograms

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