To determine if each shape can tessellate, we need to see if copies of the shape can fit together perfectly to cover a flat surface without any gaps or overlaps.
Step-by-step Analysis:
1.
Shape a (Parallelogram):
* Think about rectangles or squares; they tile a floor easily. A parallelogram is just a "slanted" rectangle.
* If you take one parallelogram and slide another one next to it, their slanted sides match up perfectly. You can keep doing this in rows, and stack the rows on top of each other.
* There are no gaps left between them.
*
Result: Yes
2.
Shape b (Circle):
* Imagine trying to cover a table with coins or plates.
* When you push circles next to each other, they touch at only one point. This leaves curved empty spaces (gaps) between every group of three or four circles.
* You cannot fill these gaps with more circles.
*
Result: No
3.
Shape d (Bowtie / Two Triangles joined at a vertex):
* Look at the pointy tips where the two triangles meet. The angle there is very sharp (acute).
* Even if you put several of these shapes together around a central point, those sharp angles won't add up to a full circle ($360^\circ$) neatly without leaving big wedge-shaped gaps or causing the shapes to crash into each other (overlap).
* Generally, shapes with inward-pointing corners (concave vertices) like this are very difficult or impossible to tessellate simply.
*
Result: No
4.
Shape e (Notched Rectangle):
* This shape looks like a rectangle with a triangle cut out of one side and added to the opposite side.
* Because the "cut out" part and the "sticking out" part are identical, you can fit the sticking-out part of one shape perfectly into the cut-out part of another shape.
* It works like a puzzle piece or a brick wall pattern. They lock together tightly with no gaps.
*
Result: Yes
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Final Answer:
a. yes
b. no
d. no
e. yes
Parent Tip: Review the logic above to help your child master the concept of tessellations worksheet printable.
