Triangle Congruence Investigation
What consecutive triangle parts need to be congruent in order to show that two triangles are congruent? Are you able to create a non-congruent pair of triangles?
Table of Contents
- Notes
- Copy of Exploring Congruency
- SSS - 3 pairs of congruent sides
- AAA- 3 pairs of congruent angles
- SAS- 2 Congruent Sides with Congruent Angle in Between
- HL- 1 Pair of Legs Congruent, 1 Pair of Hypotenuses Congruent, ONLY for right triangles
- SSA- 2 Congruent Sides with a Congruent Angle NOT in between
- ASA- 2 Pairs of Congruent Angles with a Congruent Side in between
- AAS- 2 Pairs of Congruent Angles with a Congruent Side NOT inbetween
- Card Sort
- Exit Ticket
Copy of Exploring Congruency
[b]Content Objective:[/b] I will explore and develop understanding of what criteria is required for triangle congruence.[br][b]Language Objective: [/b] I will discuss triangle congruence criteria with my table partners as I am sorting cards by their corresponding theorems.[br][br][br]
When triangles are congruent, six facts are always true.
When triangles are congruent, one triangle can be moved (through one, or more, rigid[br]motions) to coincide with the other triangle. All corresponding sides and[br]angles will be congruent.
Consider the following two triangles:
These two triangles are congruent:
[math]\bigtriangleup ABC [/math] [math]\cong\bigtriangleup[/math] KLM[br][br][b]Corresponding sides are congruent:[/b][br]AB [math]\cong[/math] KL[br]BC [math]\cong[/math] LM[br]AC [math]\cong[/math] KM[br][br][b]Corresponding angles are congruent:[/b][br]Angle A [math]\cong[/math] Angle K[br]Angle B [math]\cong[/math] Angle L[br]Angle C [math]\cong[/math] Angle M[br][br]The good news is that when proving triangles congruent, it is not necessary to[br]prove all six facts to show congruency. There are certain ordered combinations[br]of these facts that are sufficient to prove triangles congruent. These[br]combinations guarantee that, given these facts, it will be possible to construct[br]triangles which will take on only one shape (be unique), thus insuring[br]congruency.