4_3 and 4_4: Triangle Congruence
Triangle Congruence Rules
Table of Contents
- 4_3 Triangle Congruence: SSS and SAS
- SAS: Dynamic Proof!
- SSS: Dynamic Proof!
- SSA Theorem?
- 4_4 and 4_5 Triangle Congruence: ASA, AAS, and HL
- ASA Theorem?
- HL: Hypotenuse-Leg Action!
- Congruent Triangles 1
- Congruent Triangles 2
- Congruent Triangles 3
- Congruent Triangles 4
- Congruent Triangles 5
- Congruent Triangles 6
- Congruent Triangles 7
SAS: Dynamic Proof!
[color=#000000]The [/color][b][u][color=#0000ff]SAS Triangle Congruence Theorem[/color][/u][/b][color=#000000] states that [/color][b][color=#000000]if 2 sides [/color][color=#000000]and their [/color][color=#ff00ff]included angle [/color][color=#000000]of one triangle are congruent to 2 sides and their [/color][color=#ff00ff]included angle [/color][color=#000000]of another triangle, then those triangles are congruent. [/color][/b][color=#000000]The applet below uses transformational geometry to dynamically prove this very theorem. [br][br][/color][color=#000000]Interact with this applet below for a few minutes, then answer the questions that follow. [br][/color][color=#000000]As you do, feel free to move the [b]BIG WHITE POINTS[/b] anywhere you'd like on the screen! [/color]
Q1:
What geometry transformations did you observe in the applet above? List them.
Q2:
What common trait do all these transformations (you listed in your response to (1)) have?
Q3:
Go to [url=https://www.geogebra.org/m/d9HrmyAp#chapter/74321]this link[/url] and complete the first 5 exercises in this GeoGebra Book chapter.
Quick (Silent) Demo
ASA Theorem?
[color=#000000]Suppose 2 triangles have 2 pairs of congruent angles. Suppose we also know that the side between each set of given angles (in one triangle) is congruent to the side between this same pair of angles in the other triangle. [br][br]Does knowing only this constitute sufficient evidence to prove the triangles congruent? If so, explain how/why with respect to the transformations and/or triangle congruence theorems you've previously learned. If not, clearly explain why not. [/color]