Title: What you know about the Bermuda Triangle?
The basis of this lesson is for students to form a connection between the importance of geometry as it relates to the Bermuda Triangle. Students should think about the geographical locations and how they form a particular type of triangle. Within the triangle exists a relationship between the angles and the length of the sides. As the students reflect prior concepts and skills should come to mind to help them solve the problem. The ideas presented here can be used as the final lesson in a unit on triangles to summarize all that students have learned. Alternatively, the main problem from this lesson could be used as a final assessment activity for a unit on triangles.
This is a College- and Career-Ready Standards showcase lesson plan.
Standard(s): [MA2015] GEO (9-12) 10: Prove theorems about triangles. Theorems include measures of interior angles of a triangle sum to 180o, base angles of isosceles triangles are congruent, the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length, and the medians of a triangle meet at a point. [G-CO10]
Title: Location, Location, Location
In this Illuminations lesson, students use a dynamic geometry applet to investigate the relationship between the distances from a point inside a regular polygon to each side. In addition, there are links to online activity sheets and other related resources.
Standard(s): [MA2015] GEO (9-12) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1]
In this Illuminations lesson, students create parallelograms from square sheets of paper and connect them to form an octagon. During the construction, students consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and students discover a surprising result. There is also a link to a related activity sheet.
Standard(s): [MA2015] GEO (9-12) 34: Determine areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics. (Alabama)
Title: Discovering Pick's Theorem
This reproducible worksheet, from an Illuminations lesson, leads students through an investigation of Pick's Theorem using geoboards.
Standard(s): [MA2015] ALC (9-12) 11: Use ratios of perimeters, areas, and volumes of similar figures to solve applied problems. (Alabama)