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The topic Constructing triangles appears under the 7th grade (U.S.) Math Mission. This exercise constructs triangles or tries to decide why they cannot be created.

## Types of Problems

There are three types of problems in this exercise:

1. Tell whether the triangle can exist: This problem provides some information about the sides or angles of a potential triangle. The user is asked to determine if such a triangle could exist or not.
2. Tell if there is another triangle with given information: This problem describes a triangle with certain information. The user is asked to determine if another triangle with the same information could exist or not.
3. Make the triangle and tell whether another one could exist: This problem is like the previous problem but also requires the user to create a triangle using the manipulative.

## Strategies

Some geometric concepts, like the congruency theorems, could assist in doing this exercise accurately and efficiently.

1. The sum of two sides of a triangle must always exceed the third side. This is one version of what is called the Triangle Inequality.
2. The sum of all the angles in a triangle is $180^\circ$. This is called the Triangle Sum Theorem.
3. The five major triangle congruency theorems are named SSS, SAS, ASA, AAS and HL. Notably, AAA and SSA are not congruency theorems so there are potentially more than one triangle that can be made with AAA and SSA knowledge.

## Real-life Applications

1. Architects use triangles when building bridges, roofs on houses, and other structures.
2. 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.