Semi-Regular Triangular Tessellation
A semi-regular triangular tessellation is a pattern of triangles that covers a plane without any gaps or overlaps. In a semi-regular tessellation, the pattern is made up of two or more types of regular polygons, and at each vertex, the same sequence of polygons occurs.
Key Concepts
- Regular Polygon: A polygon with all sides and angles congruent. In the case of a semi-regular triangular tessellation, it involves regular triangles.
- Vertex Configuration: The sequence of polygons meeting at a vertex in the tessellation.
- Semi-Regular Tessellation: A tessellation made up of two or more types of regular polygons.
Properties
In a semi-regular triangular tessellation:
- Each vertex has the same sequence of regular polygons around it.
- The tessellation can be made up of regular triangles, squares, and hexagons.
- The sum of the angles around each vertex is 360 degrees.
Examples
Examples of semi-regular triangular tessellations include patterns made up of equilateral triangles, squares, and hexagons, such as those found in Islamic art and architecture.
Study Guide
To study semi-regular triangular tessellations, it is important to:
- Understand the properties of regular polygons and how they can be used to create tessellations.
- Practice identifying and creating different vertex configurations in semi-regular tessellations.
- Explore real-life examples of semi-regular triangular tessellations in art and architecture.
- Work on problem-solving exercises involving semi-regular tessellations.
◂Math Worksheets and Study Guides Seventh Grade. Rational and Irrational Numbers
Study Guide
Rational and Irrational Numbers 
Worksheet/Answer key
Rational and Irrational Numbers Worksheet/Answer key
Rational and Irrational Numbers Worksheet/Answer key
Rational and Irrational Numbers
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Connections to the Grade 7 Focal Points (NCTM)
Number and Operations: In grade 4, students used equivalent fractions to determine the decimal representations of fractions that they could represent with terminating decimals. Students now use division to express any fraction as a decimal, including fractions that they must represent with infinite decimals. They find this method useful when working with proportions, especially those involving percents. Students connect their work with dividing fractions to solving equations of the form ax = b, where a and b are fractions. Students continue to develop their understanding of multiplication and division and the structure of numbers by determining if a counting number greater than 1 is a prime, and if it is not, by factoring it into a product of primes.