This lesson is about right triangles and relationships between right triangles. Using an artwork by Anni Albers, students use rotations and reflections to construct and compare triangle pairs.

### Objectives

- We will come to know a right triangle and be able to differentiate it from other types of triangles.
- We will identify triangle pairs as the same based on a transformation (flip, turn, etc.).
- We will be able to describe our ideas in writing.

### Assessment

- Participation in class discussions
- Tiling with Two Shapes worksheet
- Anni’s Triangles worksheet
- Symmetrical drawings

### Time Required

1-1.5 hours

## Materials/Resources Needed

- Document camera/projector
- Art Images (linked below in the activities)
- Activity pages (4–8)
- Colored pencils or crayons
- Paper
- Pencil

## North Carolina Curriculum Alignment

After your field trip to the Asheville Art Museum, have your students talk about their visit. Encourage them to discuss artworks they saw, identifying which ones they liked the most/least and why. Ask them to talk about the studio activity and what they created.

## Activity 1: Tiling with Two Shapes

**NOTE:** *All pages referenced below are linked above in Materials/Resources Needed as “Activity pages.”*

1. Provide each student with two sheets of triangle dot paper (activity pages 4–5). This is an individual activity, but students may want to compare their drawings with others as they are working.

2. Project activity page 4 and point to the example of the two shapes in the upper right corner. Using a Smartboard or white board, show students how to draw the triangle and rhombus in the middle of the triangle dot paper (leave space between the shapes as you see in the example). Next, draw the same two shapes again, but this time with one side shared between them. Have students draw the shapes touching in the middle of their triangle dot paper. Explain that these are the shapes of two tiles that will be used to make a pattern for tiling an imaginary floor. Explain that when tiling a floor you don’t want any overlaps, gaps, or holes, so when they draw their tile design the shapes should fit together. Tell students that the goal is to make arrangements of tiles to form a pattern that can be extended across the whole floor. Tell them not to worry about the edges of the paper; we cut tiles when we get to an edge. Explain they can flip or turn the tiles as they repeat them.

4. When students have found one pattern, encourage them to find others, and then suggest they color the tiles to make a coloring pattern. Students have an extra blank sheet of triangle dot paper so that they can explore various arrangements.

5. Expect that some students will have difficulty with this activity and encourage them. You may be surprised how difficult this is for some students, and really easy for others. Use as homework and as time permits, come back to this on subsequent days. All students will have success given sufficient time.

## Activity Two: Anni’s Triangles

**NOTE:*** Read the artist biography of Anni Albers with your students before you begin the lesson*. *All pages referenced below are linked above in Materials/Resources Needed as “Activity pages.”*

1. Project *Triangulated Intaglio *by Annie Albers. Ask students to describe what they see. If students indicate that they see triangles, follow up by asking how they know it’s a triangle, how to define a triangle, and if they can identify what type of triangle they see. Discuss different types of triangles.

2. Provide students with Anni’s Triangles worksheets (activity pages 6-8). Students can begin by answering #1 and #2 based on the class discussion.

3. In the 2×2 grid shown on the bottom of activity page 6, two isosceles right triangles are touching at their vertex (point where two sides meet). Ask students to draw a different example of two isosceles right triangles touching at another vertex in the blank grid on the right. Two figures are considered the same if one will fit on top of the other by rotating or reflecting. For example, if the figure is reflected along a diagonal it is the same.

4. Move around the room looking at the students’ work and ask students to identify how their drawings are different from the example.

5. On activity page 7, ask students to draw as many different pairs of isosceles right triangles as they can in each 2×2 grid for #4. They can reference the projected artwork as inspiration. When completed, they can compare their drawings with a neighbor and explain how they are all different for #5.

6. Students should reflect on their drawings for #4 and decide if there’s a better way to organize them or put them in order. On activity page 8, students should redraw their triangle pairs in an order that they choose.

## Activity Three: Symmetry

1. Project *Dancing Dervish* by Beatrice Riese. Ask students the following questions. Make note of students’ comments about the artwork itself and of the shapes they identify.

- What’s going on in this artwork?
- Is there a difference between the top and bottom or left and right?
- Can you find any patterns?
- Does this artwork have symmetry? What kind of symmetry? This might be a good time to remind students about the different types of symmetry.
*Hint:**this artwork has rotational symmetry*.

2. Repeat the above steps using Richard Anuskiewicz’s *I* and David Hunt Jernigan’s *Fadyr T764*. Ask students the same questions first, then have them compare and contrast the three artworks.

3. Using pencil and blank paper, ask students to create an abstract design that exemplifies one type of symmetry. You can leave the assignment very general, or you can give guidelines to the amount or types of shapes/lines that they use. For example, you can limit students to using only geometric shapes and curvy lines or they can pick three shapes and two types of lines. Walk around the room and provide assistance with their drawings before providing colored pencils or crayons for coloring in their designs. Remind students that their designs should be colored symmetrically.