Special Parallelograms

1
Special Parallelograms

• Geometry
• Unit 12, Day 3
• Mr. Zampetti

2
For this lesson, you will need

• 2 index cards
• A ruler
• A protractor
• Scissors
• Piece of Tape

3
Exploration

1. Mark a point somewhere along the bottom edge of
   your index card.
2. Draw a line from that point to the top right
   corner of the rectangle to form a triangle.

Amy King
4
Exploration

1. Cut along this line to remove the triangle.
2. Attach the triangle to the left side of the
   rectangle.
3. What shape have you created?

Amy King
5
Parallelogram Properties
Diagrams from http//www.algebralab.org/lessons/l
esson.aspx?fileGeometry_QuadrilateralsSpecialChar
actieristics.xml
6
Back to your card

1. Fold along CD so that it lies along AD creating
   line ED.
2. Cut along CE and discard the excess section
   (ABEC).
3. Unfold the quadrilateral.
4. Is this a parallelogram?

E
C
Amy King
7
Back to your card

1. Measure the length of the 4 sides. What is the
   relationship of the sides?
2. Draw diagonal DE.
3. Measure ?FED, ?DEC, ?FDE, and ?CDE. What is the
   relationship of these angles?

E
F
Amy King
8
Back to your card

1. Draw diagonal FC.
2. Measure ?EFC, ?CFD, ?ECF, and ?FCD. What is the
   relationship of these angles?
3. Measure the 4 angles formed where the diagonals
   intersect. What is the measure of these angles?

E
F
Amy King
9
Properties of a Rhombus
has 4 congruent sides (def)
Diagrams from http//www.algebralab.org/lessons/l
esson.aspx?fileGeometry_QuadrilateralsSpecialChar
actieristics.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
Properties of a Rectangle
Diagrams from http//www.algebralab.org/lessons/l
esson.aspx?fileGeometry_QuadrilateralsSpecialChar
actieristics.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/len
tskari1.jpg
13
Back to the index card

1. Use your ruler to draw two diagonals of the
   quadrilateral.
2. Measure the angles formed by the side of the
   quadrilateral and the diagonal. What conjecture
   can you make about these angles?
3. What is the name of this quadrilateral?

http//www.kolumbus.fi/y602648/semisuper/kuva/len
tskari1.jpg
14
Properties of a Square
opposite angles congruent (all right)
Diagrams from http//www.algebralab.org/lessons/l
esson.aspx?fileGeometry_QuadrilateralsSpecialChar
actieristics.xml
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Complete the Chart
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Homework

• Work Packet Special Parallelograms