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

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

Exploration

Amy King

3. Cut along this line to remove the triangle.

4. Attach the triangle to the left side of the rectangle.

5. What shape have you created?

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

Parallelogram Properties:

Back to your card…

Amy King

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? C

E

Back to your card…

Amy King

5. Measure the length of the 4 sides. What is the relationship of the sides?

6. Draw diagonal DE.

7. Measure FED, DEC, FDE, and CDE. What is the relationship of these angles?

F

E

Back to your card…

Amy King

F

E

8. Draw diagonal FC.

9. Measure EFC, CFD, ECF, and FCD. What is the relationship of these angles?

10. Measure the 4 angles formed where the diagonals intersect. What is the measure of these angles?

Properties of a Rhombus

Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

has 4 congruent sides (def)

opposite sides are parallel

opposite sides are congruent

opposite angles are congruent

diagonals bisect each other

diagonals bisect opposite angles

diagonals are perpendicular

Take out a new index card…

1. Is your card a parallelogram? Why?

2. What is the relationship of the 4 angles of your card?

3. What is the name of this quadrilateral?

4. Measure the length of each diagonal. What conjecture can you make regarding the lengths of the diagonals of a rectangle?

Properties of a Rectangle

Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

opposite sides parallel

opposite sides congruent

diagonals are congruent (AC = BD)

diagonals bisect each other

has congruent (right) angles (definition)

Back to the index card…

1. Fold the corner of your card down to make a triangle. Cut off the rectangle at the bottom edge and unfold the card.

2. Is this quadrilateral A parallelogram? A rectangle? A rhombus?

http://www.kolumbus.fi/~y602648/semisuper/kuva/lentskari1.jpg

Back to the index card…

3. Use your ruler to draw two diagonals of the quadrilateral.

4. Measure the angles formed by the side of the quadrilateral and the diagonal. What conjecture can you make about these angles?

5. What is the name of this quadrilateral?

http://www.kolumbus.fi/~y602648/semisuper/kuva/lentskari1.jpg

Properties of a Square

Diagrams from: http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_QuadrilateralsSpecialCharactieristics.xml

has 4 congruent sides and 4 congruent (right) angles

opposite sides parallel

opposite angles congruent (all right)

diagonals are congruent (AC=BD)

diagonals bisect each other

diagonals bisect opposite angles all bisected angles equal 45ºdiagonals are perpendicular

Complete the Chart:

Homework

Work Packet: Special Parallelograms