Math Forum - Problems Library - Geometry - Transformations, Symmetry

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Geometry
  lines/angles
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  perimeter, area,
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  similar/congruent
  right triangles
  transform/symmetry
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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 9-12


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" six-pointed 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>>

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