D.G. 4.4 & 4.5: Triangle Congruence Shortcuts
4.4 and 4.5: Explorations for proving which "shortcuts" can be used to prove two triangles congruent.
Table of Contents
- Triangle Congruence Exploration -- Day 1
- SSS Exploration
- SAS Exploration
- SSA Exploration
- Triangle Congruence Exploration -- Day 2
- ASA Exploration
- AAA Exploration
- SAA Exploration
SSS Exploration
[b]In the exploration below:[/b][br][br]1) You will explore the Side-Side-Side (SSS) case. If the three sides of one triangle are congruent to the three sides of another, must the two triangles be congruent?[br][br]2) All of the segments in the image are set to have lengths that are congruent to their corresponding object (segment AB corresponds with A'B', BC with B'C', etc.). You are able to manipulate all three of the angles.[br][br]3) Experiment by moving the points around in order to test the theory that Side-Side-Side (SSS) is a criteria for triangle congruence.[br][br][br][b]Answer the following questions on binder paper:[/b][br][br]4) Is it possible to make a different triangle from the same three parts, or are the two triangles always congruent?[br][br]5) Based on your answer to #4, is SSS a valid "shortcut" for triangle congruence?
ASA Exploration
[b]In the given exploration:[/b][br][br]1) You will explore the Angle-Side-Angle (ASA) case. If two angles and the included ("in between") side of one triangle are congruent to two angles and the included side of another, must the two triangles be congruent?[br][br]2) The length of segment A'B' is fixed so that it always matches the length of AB. Also, the measures of the angles at A' and B' are fixed so that they always match the angles at A and B. You are free to manipulate all the vertices of triangle ABC, and the lengths of the other sides of triangle A'B'C'.[br][br]3) Experiment by moving the points around in order to test the theory that Angle-Side-Angle (ASA) is a criteria for triangle congruence.[br][br][br][b]Answer the following questions on binder paper:[/b][br][br]4) Can you find a way to make a triangle with A' and B' that looks different from triangle ABC? Explain why or why not.[br][br]5) Based on your answer to #4, is ASA a valid "shortcut" for triangle congruence?