Special Parallelograms Geometry Unit 12, Day 3 Mr. Zampetti

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. Draw a line from that point to the top right corner of the rectangle to form a triangle. Amy King

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

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

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

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

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

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

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?

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

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

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

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

Complete the Chart:

Homework Work Packet: Special Parallelograms