The Triangle Angle Sum Theorem states that the sum of the three angles in a triangle is always 180 degrees. This theorem is important for creating triangles because it ensures that the angles chosen will result in a valid triangle.
If we want to create an acute triangle, we can choose three angle measures less than 90 degrees each. For example, we could choose angles of 30°, 50°, and 70°.
If we want to create an obtuse triangle, we can choose one angle measure greater than 90 degrees. For example, we could choose angles of 100°, 40°, and 40°.
If we want to create a right triangle, we can choose one angle measure of 90 degrees. For example, we could choose angles of 90°, 30°, and 60°.
It is important to note that there are certain restrictions on the angle measures that can be chosen in order to create a valid triangle. For example, in a triangle, the measure of any one angle must be less than the sum of the measures of the other two angles.
In total, there are infinitely many possible triangles that can be created with three angle measures, as long as the angle measures satisfy the conditions for creating a triangle.
Decide if you want to make an acute, obtuse, or right triangle and select three angle measures. How is the triangle angle sum theorem important for creating triangles? How many triangles can you make with three angle measures?
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