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Mr. Wolf
Wednesday 11/5/08
Geometry
Grades 10-12
Unit 5: Quadrilaterals
Special Quadrilaterals and Trapezoids
Materials and Resources:
 Warm-up (1 per student)
 Special Quadrilaterals and Trapezoids Notes sheet (1 per student)
 Special Quadrilaterals and Trapezoids Instructor Version
 Quadrilaterals The Card Game Rules sheet (1 per student)
 Quadrilaterals The Card Game Deck (8-9 decks)
 Exit Ticket (1 per student)
PA Standards Addressed:
2.9.11 C. Identify and prove the properties of quadrilaterals involving opposite sides
and angles, consecutive sides and angles and diagonals using deductive proofs.
Instructional Objectives:
 Students will be able to identify and describe the different properties of special
quadrilaterals including trapezoids.
Time
10 min
1 min
min
Activity
Warm-up
Agenda
Special
Quadrilaterals and
Trapezoids Notes
min
Quadrilaterals The
Card Game
Description
Pass out the Warm-up and review solutions.
Review the goals for the day.
Modeling: Pass out the notes sheet and provide the
information for students to fill in.
Guiding: As a class, fill in the properties table and
the hierarchy list.
Independent Practice:
Quadrilaterals The Card Game
Assessment: HW exercises will be graded.
Modifications:
Students with special needs will be given notes
sheets that are filled in as necessary.
Advanced students will be called on when filling in
the notes sheet information.
Modeling: Pass out the rules sheets and pick two
students to do a mock round of play to illustrate
how to play the game.
Guiding: Walk around and provide help and
interpretation of the rules as necessary.
Independent Practice: Students will complete the
game.
Assessment: HW exercises will be graded.
Modifications:
1 min
Agenda
5 min
Conclusion
Homework:
Pg. 186 #1-4
Pg. 187 #11, 12, 14
Pg. 192 #1-9
Lesson Reflection:
Students with special needs will be placed in
groups with outgoing students who can help
improve their social skills.
Advanced students will be placed in groups
together to challenge each other.
Revisit goals and identify whether they were met.
Pass out the Exit Ticket and collect at the bell.
Name: ________________________
Wacky Wednesday Warm-up
Can you write the next item in the following pattern?
o, t, t, f, f, s, s, e, _____
Name: ________________________
Wacky Wednesday Warm-up
Can you write the next item in the following pattern?
o, t, t, f, f, s, s, e, _____
Name: ________________________
Wacky Wednesday Warm-up
Can you write the next item in the following pattern?
o, t, t, f, f, s, s, e, _____
Name: ________________________
Wacky Wednesday Warm-up
Can you write the next item in the following pattern?
o, t, t, f, f, s, s, e, _____
Geometry Fall 2008
Name: ________________________
Special Parallelograms and Trapezoids
Quadrilaterals Theorems:
1) The diagonals of a rectangle are congruent.
2) The diagonals of a rhombus are perpendicular.
3) Each diagonal of a rhombus bisects two angles of the rhombus.
Table of Properties
Property
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
A diagonal forms two congruent triangles.
Diagonals bisect each other.
Diagonals are congruent.
Diagonals are perpendicular.
A diagonal bisects two angles.
All angles are right angles.
All sides are congruent.
Parallelogram
Quadrilaterals Hierarchy
Rectangle
Rhombus
Square
Trapezoids
Isosceles Trapezoid:
Median:
Trapezoids Theorems:
1)
2)
3)
Example:
A trapezoid and its median are shown. Find the value of x.
Geometry Fall 2008
Name: ________________________
Special Parallelograms and Trapezoids
Instructor Version
Quadrilaterals Theorems:
1) The diagonals of a rectangle are congruent.
2) The diagonals of a rhombus are perpendicular.
3) Each diagonal of a rhombus bisects two angles of the rhombus.
Table of Properties:
Property
Opposite sides are parallel.
Opposite sides are congruent.
Opposite angles are congruent.
A diagonal forms two congruent triangles.
Diagonals bisect each other.
Diagonals are congruent.
Diagonals are perpendicular.
A diagonal bisects two angles.
All angles are right angles.
All sides are congruent.
Hierarchy:
Parallelogram
X
X
X
X
X
Rectangle
X
X
X
X
X
X
Rhombus
X
X
X
X
X
X
X
X
X
Square
X
X
X
X
X
X
X
X
X
X
Trapezoid
Trapezoids are quadrilaterals with exactly one pair of opposite sides parallel.
Isosceles Trapezoid:
Median:
The median of a trapezoid is the segment that joins the midpoints of the legs.
Trapezoids Theorems:
1) Base angles of an isosceles trapezoid are congruent.
2) The median of a trapezoid is parallel to the bases.
3) The median of a trapezoid has a length equal to the average of the base lengths.
Example:
A trapezoid and its median are shown. Find the value of x.
Geometry Fall 2008
Name: ________________________
Quadrilaterals Card Game Rules
Materials:
 Quadrilaterals Card Game Rules
 Quadrilaterals Card Game Deck
Goal:
To accumulate all of the cards in the deck.
Gameplay:
 The class will be divided into groups of 3 students each.
 Shuffle and deal the cards so that every member of the group has the same
number of cards.
 Players may not look at their cards and must keep their cards face down in a stack
in front of them.
 During each round of play, players will select the top card from their deck and
place it on their desk to “face-off” with the other players.
 The face-off in each round will have a “winner” who will collect all 4 cards and
place them on the bottom of his/her stack.
 Face-off winners of each round will be determined based on the following rules:
Round 1 Rule: The quadrilateral with diagonals that are congruent wins.
Round 2 Rule: The quadrilateral with the most right angles wins.
Round 3 Rule: The quadrilateral with the most congruent sides wins.
Round 4 Rule: The quadrilateral with diagonals that bisect two angles wins.
Round 5 Rule: The quadrilateral with only one set of opposite sides parallel.
Round 6 Rule: The quadrilateral with perpendicular diagonals wins.
After completing Round 6, go back to Round 1 and repeat the process.





Each group is responsible for keeping track of the round number.
In the event of a tie, the players who tied will take the next card from the top of
their stack and place it in front of them. The winner will be determined from this
new face-off using the same Round Rule as the initial face-off.
If a tie occurs when a player has thrown his/her last card, this player wins the
face-off.
When a player loses all of his/her cards, he/she is eliminated.
The game ends when one player has accumulated all the cards in the deck.
Geometry Fall 2008
Name: ________________________
Exit Ticket
Directions: Answer the following questions.
1) Name two shapes whose diagonals are congruent:
2) Name two shapes whose diagonals meet at right angles:
3) Name two shapes whose diagonals bisect two angles:
4) Do you feel that the game helped you to learn the properties of the figures?
5) Why or why not?
Geometry Fall 2008
Name: ________________________
Exit Ticket
Directions: Answer the following questions.
1) Name two shapes whose diagonals are congruent:
2) Name two shapes whose diagonals meet at right angles:
3) Name two shapes whose diagonals bisect two angles:
4) Do you feel that the game helped you to learn the properties of the figures?
5) Why or why not?