How to verify the sum of interior angles of a triangle using Geometry Sketchpad

Geometry Sketchpad is a powerful geometric drawing software that can be used to verify the sum of the interior angles of a triangle. PHP editor Youzi will introduce in this article how to use the geometric sketchpad to verify the sum of the interior angles of a triangle. By using the geometric sketchpad to accurately measure angles, everyone can intuitively understand the rules of the sum of the interior angles of a triangle. This article will explain the steps step by step and guide you to explore the mystery of the sum of the interior angles of a triangle.

Create a new geometric sketchpad file. Draw a triangle ABC and set the line segments as dotted lines. Construct the midpoints D and E of line segments AB and AC. Draw perpendiculars to line segment BC through points A, D, and E. The vertical feet are F, G, and H respectively. Hide the perpendiculars and set the line segments DG, GH, HE, and ED as solid lines.

Draw points I, J, K arbitrarily, and draw line segments ID, IE, JD, JG, KE, KH.

Select points I, A, J, B, K, C in sequence, select [Edit]-[Operation Button]-[Move] command, and change the label to [Restore] . Select points I and F, select [Edit] - [Operation Button] - [Move] command, and change the label to [Upper Corner Close]. Select points J and F, select [Edit] - [Operation Button] - [Move] command, and change the label to [Left Corner Close]. Select points K and F, select [Edit]-[Operation Button]-[Move] command, and change the label to [Right Corner Close].

Draw line segment AF, set to dashed line. Fill the interior of triangle IDE, triangle JDG, triangle EHK, and quadrilateral DEHG with yellow.

Select the [File]-[Save] command. When clicking the [Restore] button, the effect is as shown in the figure.

Click the [Upper Corner Close] button, [Left Corner Close] button, and [Right Corner Close] button in sequence, the effect is as shown in the figure.

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