To solve this problem, we need to understand what a tessellation is. A tessellation is a pattern of shapes that fit together perfectly without any gaps or overlaps. The shapes cover the entire plane continuously.
Let's analyze each pattern one by one:
(i) This pattern shows hexagons arranged in rows. Each hexagon fits snugly against its neighbors. There are no gaps between them, and they do not overlap. This is a classic example of a tessellation using regular hexagons.
(ii) This pattern shows wavy, bird-like shapes. Looking closely at how they fit together, the "beak" of one shape fits perfectly into the "tail" of the next. They interlock to cover the area completely without leaving any empty space or overlapping. This is a tessellation.
(iii) This pattern shows regular hexagons again. However, unlike pattern (i), there are clear gaps between the hexagons. The shapes do not touch each other completely, leaving empty spaces. Because there are gaps, this is
not a tessellation.
(iv) This pattern shows a grid of shapes that look like rounded rectangles or capsules. They are arranged in rows and columns. Each shape touches its neighbors, and they fill the entire rectangular area without any gaps or overlaps. This is a tessellation.
Summary:
- Pattern (i): Yes, it is a tessellation.
- Pattern (ii): Yes, it is a tessellation.
- Pattern (iii): No, it is not a tessellation because there are gaps.
- Pattern (iv): Yes, it is a tessellation.
Final Answer:
(i) Yes
(ii) Yes
(iii) No
(iv) Yes
Parent Tip: Review the logic above to help your child master the concept of tessellation worksheet 7th grade answers.
