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Special Parallelograms

Special Parallelograms. Geometry Unit 12, Day 3 Ms. Reed. For this lesson, you will need:. 2 index cards A ruler A protractor Scissors Piece of Tape. Exploration. Mark a point somewhere along the bottom edge of your index card.

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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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