Proving Rectangles: Area and Perimeter of Polygons in a Coordinate Plane

This GeoGebra example demonstrates how to prove a quadrilateral is a rectangle by calculating the side lengths, area, and perimeter of polygons placed in a coordinate plane. The core mathematical concepts involve coordinate geometry, the distance formula, rectangle criteria (e.g., opposite sides equal and diagonals equal, or all angles are right angles), and formulas for polygon area and perimeter. Construction highlights: users place vertices using point tools, connect them with line segments, then employ measurement commands (such as distance or length) to obtain side lengths and the area tool to compute the enclosed region, thereby verifying the rectangle properties. This resource is suitable for upper middle school or high school students, reinforcing analytic geometry skills and logical deduction from coordinate data. It serves well for classroom demonstrations or independent student exploration.