To determine whether each shape can tessellate, we need to check if the shape can be repeated in a pattern such that there are no gaps or overlaps between the shapes. Let's analyze each shape step by step:
---
Shape a: Parallelogram
- A parallelogram can tessellate because it can be arranged in a grid-like pattern where each side of one parallelogram perfectly aligns with the corresponding side of an adjacent parallelogram.
-
Answer: Yes
---
Shape b: Circle
- Circles cannot tessellate because there will always be gaps between them when they are placed next to each other. No matter how you arrange circles, there will be spaces that cannot be filled by another circle.
-
Answer: No
---
Shape c: Star (Five-pointed star)
- A five-pointed star generally does not tessellate because its points and edges do not fit together seamlessly without gaps or overlaps. The irregular angles and shapes of the star make it impossible to fill a plane completely.
-
Answer: No
---
Shape d: Diamond (Rhombus)
- A rhombus (diamond) can tessellate because it is essentially a type of parallelogram. Like a parallelogram, it can be arranged in a grid-like pattern where each side aligns perfectly with adjacent sides.
-
Answer: Yes
---
Shape e: Arrowhead
- An arrowhead can tessellate because it has straight edges that can align with other arrowheads to form a continuous pattern without gaps or overlaps. The symmetry and angles of the arrowhead allow for this.
-
Answer: Yes
---
Shape f: Rectangle
- A rectangle can tessellate because it can be arranged in a grid-like pattern where each side of one rectangle perfectly aligns with the corresponding side of an adjacent rectangle.
-
Answer: Yes
---
Shape g: Triangle
- A triangle can tessellate because any triangle can be used to tile a plane without gaps or overlaps. Triangles have the property that their angles sum to 180 degrees, allowing them to fit together seamlessly.
-
Answer: Yes
---
Shape h: Crescent Moon
- A crescent moon shape generally cannot tessellate because its curved and irregular edges do not align well with other crescent moons. There will be gaps or overlaps when trying to arrange them.
-
Answer: No
---
Shape i: Square
- A square can tessellate because it can be arranged in a grid-like pattern where each side of one square perfectly aligns with the corresponding side of an adjacent square.
-
Answer: Yes
---
Final Answers:
- a:
Yes
- b:
No
- c:
No
- d:
Yes
- e:
Yes
- f:
Yes
- g:
Yes
- h:
No
- i:
Yes
Boxed Answer:
\[
\boxed{\text{a: Yes, b: No, c: No, d: Yes, e: Yes, f: Yes, g: Yes, h: No, i: Yes}}
\]
Parent Tip: Review the logic above to help your child master the concept of tessellation worksheet 7th grade answers.
