| Reason about the triangle congruence postulates | |
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| Description | |
| Exercise Name: | Reason about the triangle congruence postulates |
| Math Missions: | High school geometry Math Mission |
| Types of Problems: | 1 |
The Reason about the triangle congruence postulates exercise appears under the High school 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:
- 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.
Determine whether there is a congruency postulate
Strategies[]
Knowledge of congruency postulates would ensure accuracy on this exercise, and efficiency can be done by not overworking the exercise.
- Congruency is an equivalence relation. It means that all sides and angles have the same measure.
- The correct congruency postulates are SSS, SAS, ASA, AAS and (HL).
- AAA and SSA are not congruency postulates so alternate triangles can be formed.
- The triangles constructed do not need to be superimposed on the original triangle for credit.
Real-life Applications[]
- Recognizing when shapes are congruent, and conditions that ensure congruency, is an important skill in drafting and architecture.
- Architects use lots of geometry when building bridges, roofs on houses, and other structures.
- The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.