IM 6.1.10 Lesson: Bases and Heights of Triangles

① This example is a lesson from Illustrative Mathematics Grade 6, Unit 1, Lesson 10, demonstrating how to identify the base and corresponding height of a triangle and visualizing their perpendicular relationship. ② The core mathematical concept is the definition of base and height in the triangle area formula (Area = 1/2 × base × height), emphasizing that the height is the perpendicular segment from a vertex to the opposite side (or its extension), and that each triangle has three possible base-height pairs. ③ Construction notes: Although no specific GeoGebra commands are listed in the summary, typical construction involves using the polygon tool to create a triangle, the perpendicular line tool to draw the height from a vertex to the opposite side, and possibly labels for base and height, along with draggable points or sliders to change the triangle's shape and observe how base and height affect the area. ④ This is suitable for upper elementary or middle school students learning the basics of triangle area, and can be used for classroom demonstration or student exploration to deepen understanding of the base-height correspondence and the geometric meaning of area calculation.