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
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. Parallelogram Properties:
opposite sides parallel
opposite side congruent
opposite angles are congruent
diagonals bisect each other
Diagrams from:

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. 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:

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
opposite sides parallel
opposite sides congruent
has congruent (right) angles (definition)
diagonals bisect each other
diagonals are congruent (AC = BD)
Diagrams from:

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?

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?

14. 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:

15. Complete the Chart:

16. Homework
Work Packet: Special Parallelograms