Polygons in Stained Glass
Geometry
Performance Assessment E
Problem Stimulus
“What are you planning for your geometry project?” asked Joni.
“I’m going to construct a mobile showing the different kinds of triangles,” replied Darrell. “What
are you planning for your project?”
“I’m going to design a stained-glass window made of polygons,” replied Joni. “I think I’ll
concentrate on the quadrilateral family since we just studied that in math class. My mother will
help me turn my design into a small stained-glass window.”
That night, Joni used the Internet to research the special polygons that are members of the
polygon family. “We have studied quadrilaterals, parallelograms, rectangles, rhombuses,
squares, and trapezoids,” Joni shared with her mother. I have found two more quadrilaterals that
we did not study, and I want to use them in my stained-glass design. Look at this information I
found on kites and darts!”
Joni showed her mother the following information from a website:
Kite: A kite is a convex quadrilateral that gets its name from the shape of many traditional toy
kites. A kite is a quadrilateral with two pairs of equal adjacent sides. In other words, the two
sides of equal measure meet at the vertex of an angle in the figure. Here are some examples
of kites:
Dart: A dart is a concave quadrilateral with two pairs of adjacent, equal sides. It is named “dart”
because it looks like an arrowhead. A dart is also called a “deltoid.”
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Polygons in Stained Glass
Geometry
Performance Assessment E
Joni said, “I’m not sure what “concave” and “convex” mean, but from looking at the examples,
I’d say that “concave” means “caved in” while “convex” is “not caved in.”
“That’s pretty accurate,” replied Mom. “Now you are ready to create your design on the
coordinate grid.”
Joni designed her window on a coordinate plane. She numbered some of the larger pieces in
the design. This is Joni’s design.
16
15
14
y
1
7
13
12
2
11
8
6
10
9
14
9
8
7
6
5
4
3
2
12
5
3
4
10
1
0
16
15
13
11
x
1 2 3 4 5 6 7 8 9 101112131415161718 19
Task Overview
Joni created a design for a stained-glass window using mostly quadrilaterals. Use Joni’s design
to answer questions and then create an original design. Also, use attributes to name a new
quadrilateral.
Performance Task
Part A
Answer the following questions using Joni’s design.
1. Which of the numbered shapes in Joni’s design is not a quadrilateral? _________________
Explain how you know it is not a quadrilateral. _______________________________________
_______________________________________________________________________________
What is the name of this polygon? _________________________________________________
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Polygons in Stained Glass
Geometry
Performance Assessment E
2. Which of the numbered shapes in Joni’s design appears to be a rhombus?
_______________________________________________________________________________
Explain why you selected this shape. _______________________________________________
_______________________________________________________________________________
3. According to the definition Joni shared with her mother, which figure appears to be a dart?
_______________________________________________________________________________
_______________________________________________________________________________
Explain why you selected this shape. _______________________________________________
_______________________________________________________________________________
4. According to the definition Joni shared with her mother, which figure appears to be a kite?
_______________________________________________________________________________
_______________________________________________________________________________
Explain why you selected this shape. _______________________________________________
_______________________________________________________________________________
5. How are a kite and a dart alike? How are they different?
_______________________________________________________________________________
_______________________________________________________________________________
6. Is a rhombus a special type of kite? ________________________________________________
Justify your answer. ______________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
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Polygons in Stained Glass
Geometry
Performance Assessment E
Part B
Use the clues and Joni’s design to find the answer to these riddles. (Use the numbered pieces
only.) Then, write the ordered pairs that name the coordinates of the vertices of an example of
each figure in Joni’s design.
1. This quadrilateral is both a rhombus and a rectangle.
Name of figure: __________________________________________________________________
Coordinates of Vertices: __________________________________________________________
2. This quadrilateral has a pair of parallel sides, but is not a parallelogram.
Name of figure: __________________________________________________________________
Coordinates of Vertices: __________________________________________________________
3. This quadrilateral is a parallelogram with right angles, but is not a square.
Name of figure: __________________________________________________________________
Coordinates of Vertices: __________________________________________________________
Part C
Write these words in the appropriate region of this Venn diagram.
dart
octagon
rhombus
hexagon
pentagon
square
kite
rectangle
trapezoid
Polygons
Quadrilaterals
Parallelograms
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Polygons in Stained Glass
Geometry
Performance Assessment E
Part D
1. Use a ruler to design your own stained glass window on the coordinate grid below. Use
a variety of triangles, including triangles from the following categories: scalene triangle,
isosceles triangle, equilateral triangle, acute triangle, obtuse triangle, right triangle. In
addition to the ruler, you may also use the triangles from pattern blocks, tangrams, or
attribute blocks as stencils. Number each triangle in your design.
16
y
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
x
1 2 3 4 5 6 7 8 9 10111213141516
2. Complete this chart for your design.
Triangle Chart
Type of Triangle
Numbers from Design
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Acute Triangle
Right Triangle
Obtuse Triangle
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Polygons in Stained Glass
Geometry
Performance Assessment E
3. Do you have any triangles that are both right and scalene? _____________________________
Which numbers? ________________________________________________________________
Describe any other triangles that fall into more than one category by listing the triangle
number(s) and the categories.
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
________________________________________________________________________________
Part E
Joni read about two special quadrilaterals, the kite and the dart. A hexagon is a polygon that has
6 sides and 6 angles. These attributes also belong to a subcategory of hexagons called regular
hexagons. Regular hexagons are hexagons in which all sides are congruent and all angles are
congruent.
1. In the space below, design and name a special hexagon.
Draw 2 examples of your hexagon. Then, name 4 attributes about your special hexagon.
Name of hexagon:________________________________________________________________
Two examples:
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Polygons in Stained Glass
Geometry
Performance Assessment E
2. Four attributes of my special hexagon:
1.
2.
3
4.
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