Question
Can a concave quadrilateral like the one at right tile the plane? Try it. Create your own concave quadrilateral and try to create a tessellation with it. Decorate your drawing.CAN'T COPY THE FIGURE
Step 1
Let's denote the vertices as A, B, C, and D. The concave part of the quadrilateral is represented by the vertex C. Show more…
Show all steps
Your feedback will help us improve your experience
Jay Patel and 64 other Geometry educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Mini-Investigation Cut out a small nonsymmetric concave quadrilateral. Number the vertices. Use your cut-out as a template to create a tessellation. Trace about 10 images that fit together to cover part of the plane. Number the vertices of each image to match the numbers on your cut-out. a. Draw two different translation vectors that map your tessellation onto itself. How do these two vectors relate to your original quadrilateral? b. Pick a quadrilateral in your tessellation. What transformation will map the quadrilateral you picked onto an adjacent quadrilateral? With that transformation, what happens to the rest of the tessellation?
Geometry as a Mathematical System
Similarity Proofs
The figure shows a Saccheri quadrilateral on a sphere. Note that it has four sides $\overline{\text { with } \overline{C T}} \perp \overline{T R}, \overline{A R} \perp \overline{T R},$ and $\overline{C T} \cong \overline{A R}$ Can a rectangle exist in non-Euclidean geometry? Explain.
Quadrilaterals
Rectangles
Use copies of the rectangle to show how a rectangle could: a. tile the plane. b. not tile the plane.
Area and Surface Area
Tiling the Plane
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD