Triangle Congruence Investigation
What consecutive triangle parts need to be congruent in order to show that two triangles are congruent? These applets allow students to explore whether triangle relationships (SSS, AAA, SAS, HL, SSA, ASA, AAS) force triangles to be congruent or not. Are you able to create a non-congruent pair of triangles?
Table of Contents
- Do I need all these pieces?
- Make that Triangle
- Introduction
- Proof by contradiction
- Pieces of information
- 3 pairs of congruent sides
- 3 pairs of congruent angles
- Congruent Angle in Between 2 Congruent Sides with
- Congruent Angle NOT in between 2 Congruent Sides with a
- 2 Pairs of Congruent Angles with a congruent Side in between
- 2 Pairs of Congruent Angles with a Congruent Side NOT inbetween
Make that Triangle
Directions: Try to create the triangle using the least about of information. Once the triangle is created check to make sure all the pieces do work .
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[b][u]Segments: [/u][/b] [color=#0000ff][b]Blue[/b][/color] point lets you pick up and move[br] [color=#cc0000][b]Red[/b] [/color]point lets you rotate[br][br][b][u]Angles: [/u][/b] [color=#c27ba0][b]Pink[/b][/color]point lets you pick up and move it[br] [color=#f1c232][b]Yellow[/b] [/color]point lets you rotate
Proof by contradiction
Steps
[list=1][*][color=#980000]Assume your statement to be false.[br][/color][/*][*][color=#980000]Proceed as you would with a direct proof.[br][/color][/*][*][color=#980000]Come across a contradiction.[br][/color][/*][*][color=#980000]State that because of the contradiction, it can't be the case that the statement is false, so it must be true.[/color][br][/*][/list]
We are going to assume in all the scenarios that we can NOT create a triangle with the given information.
[color=#980000]If we can not create a differnt triangle, than we know that the information given is enough to create congruent triangles[br][br] If we are able to create a different triangle than we know that we can not create congruent triangles with that information.[/color]