Standard: HSG.CO.D13 – Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Grade level: High School: Geometry
Subject: Mathematics
Domain: Congruence
Teacher Overview
This standard focuses on constructing regular polygons—equilateral triangles, squares, and hexagons—inscribed in a circle. This skill is fundamental in understanding the properties of regular polygons and their relationships with circles. Mastery of this standard reinforces students’ understanding of congruence and geometric constructions, which are essential in higher-level mathematics and various real-world applications. Students should understand basic geometric shapes, properties of circles, and congruence. Familiarity with using a compass and straightedge for constructions is also necessary.
Students will be able to apply their knowledge to more complex geometric constructions and understand the properties of more advanced geometric figures.
Common Misconception 1
Some students may think that the side lengths of the inscribed polygons can vary. This is incorrect because regular polygons have all sides and angles equal.
Intervention 1
Engage students in hands-on activities using compass and straightedge to construct these polygons, emphasizing the equality of side lengths.
Common Misconception 2
Another common misconception is that the vertices of the inscribed polygons do not need to touch the circle. This is incorrect as each vertex must lie on the circle’s circumference.
Intervention 2
Utilize visual aids and dynamic geometry software to demonstrate that each vertex of the inscribed polygon must touch the circle.
Prerequisite Knowledge
Students should have an understanding of basic geometric shapes, properties of circles, and the concept of congruence. They should also be familiar with using a compass and straightedge for geometric constructions.
Subsequent Knowledge
After mastering this standard, students will be able to apply their knowledge of geometric constructions to more complex problems, such as constructing tangents to circles, inscribing polygons within other polygons, and understanding the properties of more complex geometric figures.
Instructional Activities
- Constructing inscribed polygons using compass and straightedge
- Using dynamic geometry software to visualize inscribed polygons
- Exploring real-world applications of inscribed polygons in art and architecture
- Creating tiling patterns with inscribed polygons
- Investigating the properties of inscribed polygons through hands-on activities
