Reason about the triangle congruence postulates

The  exercise appears under the Geometry Math Mission. This exercise explores the congruency postulates and constructs counterexamples in the cases that they fail to increase understanding.

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine whether there is a congruency postulate: This problem provides a given triangle with certain fixed attributes. The student is asked to use another set of pieces to determine if there are one or several triangles that have the same properties.Conpost1.png

Strategies
Knowledge of congruency postulates would ensure accuracy on this exercise, and efficiency can be done by not overworking the exercise.
 * 1) Congruency is an equivalence relation. It means that all sides and angles have the same measure.
 * 2) The correct congruency postulates are SSS, SAS, ASA, AAS and (HL).
 * 3) AAA and SSA are not congruency postulates so alternate triangles can be formed.
 * 4) The triangles constructed do not need to be superimposed on the original triangle for credit.

Real-life Applications

 * 1) Recognizing when shapes are congruent, and conditions that ensure congruency, is an important skill in drafting and architecture.