Objective:

Use GeoGebra to explore and demonstrate the three methods for proving triangle congruence: Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Side-Side-Side (SSS).

Directions:

1. Open GeoGebra:

   • Launch the GeoGebra software on your device.

2. Create a Triangle:

   • Select the Polygon Tool from the toolbar.

   • Click three points on the grid to create a triangle. Label the vertices as A, B, and C.

3. Explore Side-Angle-Side (SAS):

   • Create a second triangle by selecting the Polygon Tool again.

   • Click to create points D, E, and F such that:

     • AB = DE

     • \angle ABC = \angle DEF

     • AC = DF

   • Use the Angle Tool to measure the included angle and ensure it is equal.

   • Show that triangles ABC and DEF are congruent by using the SAS method.

4. Explore Angle-Side-Angle (ASA):

   • Create another triangle using the Polygon Tool.

   • Label the vertices as G, H, and I such that:

     • \angle GHI = \angle ABC

     • GH = AB

     • \angle HIG = \angle ACB

   • Measure the angles using the Angle Tool to confirm they are equal.

   • Demonstrate congruence using the ASA method.

5. Explore Side-Side-Side (SSS):

   • Create a final triangle and label the vertices as J, K, and L such that:

     • JK = AB

     • KL = BC

     • JL = AC

   • Use the Segment Tool to measure all sides and ensure they are equal.

   • Show that triangles ABC and JKL are congruent using the SSS method.

6. Document Your Findings:

   • For each triangle pair, write a brief explanation of how you proved their congruence using the respective method.

   • Include screenshots of your triangles in your document.

7. Share Your Work:

   • Prepare to present your findings to the class, explaining each method and your conclusions.

Tips:

• Use the Move Tool to adjust the triangles and see how they remain congruent.

• Experiment with different triangle shapes and sizes to deepen your understanding.

• Make sure to save your work periodically!

Questions to Consider:

• How do the properties of the triangles change when you manipulate their shapes?

• Why is it important to have the correct order of sides and angles when using these methods?

Submission:

• Turn in your document with explanations and screenshots by the end of class.

Happy exploring!