TOPICS
This page:
transformations/symmetry
About Levels
of Difficulty
Geometry
lines/angles
triangles
quadrilaterals
polygons
circles
perimeter, area,
volume
similar/congruent
right triangles
transform/symmetry
construction/locus
coordinate geometry
modeling/applications
Browse all
Geometry
Problems
Geometry
Home
About the
PoW Library


Transformations and Symmetry

Basic properties of transformations and symmetry are explored in
this section.
Geometry can be thought of as the study of shapes and their transformations.
The problems in this section explore the concepts of reflection, translation,
rotation, and/or dilation, from visual and algebraic perspectives. Since the
high school curriculum does not always address these topics, some of the
problems will provide definitions or explanatory references.
 Related Resources

Interactive resources from our Math Tools project:
Geometry: Transformations and Symmetry
The closest match in our Ask Dr. Math archives:
High School: Symmetry/Transformations
NCTM Standards:
Geometry Standard for Grades 912
Access to these problems requires a Membership.

Clever Cuts
 Annie Fetter

Geometry, difficulty level 2. Find three different ways to cut a hexagonal cake into six congruent
pieces.
... more>>

Dilating a Quadrilateral
 Annie Fetter

Geometry, difficulty level 3. Given two similar quadrilaterals on a coordinate grid, determine the ratio and center of dilation.
... more>>

Eminen
 Annie Fetter

Geometry, difficulty level 3. Figure out what size squares will tile a rectangle.
... more>>

Exploding Shapes
 Annie Fetter

Geometry, difficulty level 2. How will Clarissa finish her dilation?
... more>>

A Line of Reflection
 Annie Fetter

Geometry, difficulty level 2. Find the equation of the line of reflection for triangle ABC and its
image, A'B'C'.
... more>>

Making a Six Pointed Star
 Annie Fetter

Geometry, difficulty level 3. Take a circle of paper. Explain how to fold it so that you can make just one cut and get a "perfect" sixpointed star.
... more>>

Mirror, Mirror
 Annie Fetter

Geometry, difficulty level 2. In the given image, the green polygon is a reflection of the purple
polygon. Find the equation of the line of reflection.
... more>>

Point P Perambulates
 Annie Fetter

Geometry, difficulty level 3. Find the length of the path of a vertex of an equilateral triangle as that triangle rotates around the inside of a square.
... more>>

The Rolling Triangle
 Annie Fetter

Geometry, difficulty level 3. Equilateral triangle ABC sits on top of unit square DEFG so that AC is
coincident with DE. The triangle is rotated around the outside of the
square until it returns to the top edge. How far did point A travel?
... more>>

Rotating a Triangle
 Annie Fetter

Geometry, difficulty level 2. Given a triangle on a coordinate grid, find the new coordinates of the vertices if you rotate the triangle 90 degrees about the origin.
... more>>

Similar Perimeter
 Annie Fetter

Geometry, difficulty level 2. Find the coordinates of the vertices of a triangle similar to the
given triangle with the designated perimeter.
... more>>

A Tale of Two Transformations
 Annie Fetter

Geometry, difficulty level 3. Compare the results of these two transformations on the coordinate plane.
... more>>

Transforming a Triangle
 Annie Fetter

Geometry, difficulty level 1. Given two triangles on a coordinate plane, find a pair of transformations that will map the first triangle onto the second triangle.
... more>>

Triangle in Motion?
 Annie Fetter

Geometry, difficulty level 2. Given triangle ABC, the triangle is translated and then reflected, and
the locations of A' and A'' are given. Find the locations of B'' and C''.
... more>>

Triangle Transformation
 Annie Fetter

Geometry, difficulty level 3. Given triangles ABC and DEF on the coordinate plane and a list of transformations, explain how to map ABC onto DEF in only two steps.
... more>>
Page: 1
