InterMath | Workshop Support | Write Up Template
Title:
Mystery Quadrilaterals
Problem Statement
Some quadrilaterals have special names because they have some special properties. For example, a
rectangle is any quadrilateral with four right angles. Alternately, a rectangle is a parallelogram with 1 right
angle (Can you explain why?) A square is "more special" than a rectangle because it has four right angles
and four equal sides (so a square is a special rectangle.)
Each of the Geometer's Sketchpad files below contains a different quadrilateral. Your goal is to use your
knowledge about quadrilateral properties and the Measure menu in Geometer's Sketchpad to determine
the MOST specific name of each quadrilateral.
Be careful! All of the quadrilaterals will look like squares, but only one of them will actually be a square.
Justify each of your responses by including properties of the quadrilateral that make it unique.






Mystery
Mystery
Mystery
Mystery
Mystery
Mystery
Quadrilateral
Quadrilateral
Quadrilateral
Quadrilateral
Quadrilateral
Quadrilateral
1
2
3
4
5
6
Problem setup:
Examine the six quadrilaterals that were provided in the Intermath problem. Through examination, I will be
able to label the quadrilaterals. One of the six will be a square. I will measure angles and side lengths. You
will use your knowledge of quadrilateral properties and determine a name of each quadrilateral, based on its’
properties.
Plans to Solve/Investigate the Problem :
Using Intermath and GSP, I will open the six provided quadrilaterals. I will examine the properties of each
quadrilateral. I will measure each angle and side length to help me determine the name for the different shapes.
I will justify my response by discussing the properties of each quadrilateral. One and only one of the
quadrilaterals will be a square.
Investigation/Exploration of the Problem :
Using Geometer’s Sketchpad and the Intermath web site, I will look at and investigate the six provided
quadrilaterals. I pulled up the Mystery Quadrilateral one by one and measured each of the angles and side
lengths to determine the properties of each quadrilateral.
MYSTERY
QUADRILATERAL 1
B
j = 4.17 cm
BC = 4.17 cm
k = 4.24 cm
AD = 4.17 cm
j
A
BC
mABC = 91.00
C
AD
mBCD = 89.01
mCDA = 89.99
mDAB = 90.00
k
D

Mystery Quadrilateral 1: The figure above is not a square because all four sides are not equal and all
four angles are not 90 degrees. The figure is not a rectangle because it does not have two pairs of
congruent sides or four right angles. There is a pair of parallel sides - segment AB and segment DC are
parallel. Since there are two sides that are parallel, this shape is a trapezoid.
MYSTERY QUADRILATERAL 2
j = 5.86 cm
q = 5.91 cm
r = 5.86 cm
s = 5.91 cm
B
A
j
q
s
C
D

mDAB = 90.00
mABC = 90.00
mBCD = 90.00
mCDA = 90.00
r
Mystery Quadrilateral 2: This quadrilateral directly above is classified as a parallelogram. The
properties fit the criteria of a parallelogram by having two pair of opposite sides that are parallel to each
other. This parallelogram is also a rectangle - it has four right angles and two pairs of parallel lines.
This figure cannot be a square because the four equals are right angles but the four sides are not
congruent.
MYSTERY QUADRILATERAL 3
B
mCAB = 90.00
mABD = 90.00
CB
mBDC = 90.00
D mDCA = 90.00
m
o = 4.71 cm
CB = 4.71 cm
m = 4.71 cm
A
p = 4.71 cm
p
o
C

Mystery Quadrilateral 3: This figure’s sides are congruent and it has 4 right angles. The opposite sides
have the same slope. This quadrilateral is a square.
MYSTERY
QUADRILATERAL 4
B
mABC = 91.00
mBCD = 89.00
BA
BC
mCDA = 91.00
mDAB = 89.00
A
C
BA = 3.92 cm
BC = 3.92 cm
CD
k
D

CD = 3.92 cm
k = 3.92 cm
Mystery Quadrilateral 4: This figure is a parallelogram. There are four congruent sides and two pairs of
congruent angles. This qualifies this quadrilateral as a rhombus.
MYSTERY
QUADRILATERAL 5
A
B
mCAB = 89.06
AB
mABD = 90.94
mBDC = 89.06
mDCA = 90.94
AB = 2.30 in.
l = 2.25 in.
n = 2.30 in.
l
m = 2.25 in.
m
D
n
C

Mystery Quadrilateral 5: This quadrilateral has two pairs of congruent sides. This figure cannot be a
square or a rectangle because it doesn’t have four equal angles and not a rhombus because it doesn’t
have four equal sides. There are two pairs of congruent angles and two pairs of parallel sides. This
shows that this quadrilateral is a parallelogram.
MYSTERY
QUADRILATERAL 6
D
AD = 4.27 cm
CD = 4.27 cm
AD
A
BC = 4.23 cm
AB = 4.23 cm
CD
AB
mADC = 91.00
mDCB = 88.42
mCBA = 92.15
B

BC
C
mBAD = 88.42
Mystery Quadrilateral 6: This figure is a convex kite. It has 2 pairs of different but equal adjacent sides.
This quadrilateral cannot be a square or rectangle because none of the angles are 90 degrees.
GPS:
Geometry
Students will further develop their understanding of plane and solid geometric figures, incorporating the
use of appropriate technology and using this knowledge to solve authentic problems.
M6G1. Students will further develop their understanding of plane figures.
a. Determine and use lines of symmetry.
d. Interpret and sketch simple scale drawings.
e. Solve problems involving scale drawings.
Measurement
M6M2. Students will use appropriate units of measure for finding length, perimeter, area and volume and
will express each quantity using the appropriate unit.
Process Standards
P1. Students will solve problems (using appropriate technology).
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
P2. Students will reason and evaluate mathematical arguments.
a. Recognize reasoning and proof as fundamental aspects of mathematics.
b. Make and investigate mathematical conjectures.
c. Develop and evaluate mathematical arguments and proofs.
d. Select and use various types of reasoning and methods of proof.
P3. Students will communicate mathematically.
a. Organize and consolidate their mathematical thinking through
communication.
b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
c. Analyze and evaluate the mathematical thinking and strategies of others.
d. Use the language of mathematics to express mathematical ideas precisely.
P4. Students will make connections among mathematical ideas and to other disciplines.
a. Recognize and use connections among mathematical ideas.
b. Understand how mathematical ideas interconnect and build on one another to produce a coherent
whole.
c. Recognize and apply mathematics in contexts outside of mathematics.
P5. Students will represent mathematics in multiple ways.
a. Create and use representations to organize, record, and communicate mathematical ideas.
b. Select, apply, and translate among mathematical representations to solve problems.
c. Use representations to model and interpret physical, social, and mathematical phenomena.
Extensions of the Problem:
Have students construct particular quadrilaterals based on specific properties given to them. This could help
you to observe and have an assessment of the Van Heile levels your students are on.
Some examples:
1. Create a quadrilateral with four right angles and four equal sides. What am I?
2. Create a quadrilateral with four right angles and two pairs of equal sides. What am I?
3. Create a quadrilateral with two pairs of different but equal adjacent sides and no equal angles. What am
I?
4. Create a quadrilateral with two pairs of congruent angles and two pairs of equal sides. What am I?
5. Create a quadrilateral with four congruent sides and two pairs of congruent angles. What am I?
6. Create a quadrilateral with only two sides that are parallel. What am I?
Author & Contact:
Mandie Pulley
mandie_pulley@yahoo.com
Important Note: You should compose your write-up targeting an audience in mind rather than just the
instructor for the course. You are creating a page to publish it on the web.