MLS                                                                                                               Yolanda Volcimus
Harvard                                                                                                        10/14/12
                                                                           Journal Entry

              Prompt: Describe your understanding of the Triangle Sum Theorem. What does it say about the angles of a triangle? How can you use the Triangle Sum Theorem to prove 3 angle measurements are the angles of a triangle? Can the theorem be used to prove that 3 anglemeasurements are not the angles of a triangle? Apply your understanding of the Triangle Sum Theorem to answer the following scenario. 

             Triangle LMN is an obtuse triangle and m < L = 25 degrees. m < M is the obtuse angle, and its measure in degrees is a whole number. What is the largest m < N can be to the nearest whole degree?

            Answer: The Triangle Sum Theorem indicates that "The angle measures of a triangle adds up to 180 degrees." Three types of triangles are: Equilateral Triangle, Issosceles Triangles, and Scalene Triangles. Equilateral Triangle has three congruent sides and three congruents angles. An Issoscele Triangle has at least two congruent sides and two congruent angles. Also, an Scalene Triangle has no congruent sides nor angles. I can use the Triangle Sum Theorem to prove three measurements are the angles of a triangles because the Triangle Sum Theorem acknowledged that the sum of the angles in a triangle equals 180 degrees. For example: if a scalene triangle has the measurements of 50 degrees, 60 degrees, and 70 degrees, I know these three measurements are the angles of that triangle because the sum of 50, 60, and 70 is 180 [50+60+70=180]. Thus, I can utilize the Triangle Sum Theorem to prove that three measurements are the angles of a triangle.

           Yes, the theorem can be used to prove that three anglemeasurements are not the angles of a triangle. For instant, three angles of a triangle are: 30, 50, and 40. I used the theorem to determine wether the three anglemeasurements are the angles of a triangle. The sum of 30, 50, and 40 is 120 [30+50+40=120]. This prove that the anglemeasurements are not the angles of the triangle because the sum of the angles does not equal 180 degrees. 

         The largest m < N can be to the nearest whole degree is 64 degrees because if <L is 25 degrees, <M can be 91 degrees because an obtuse angle is an angle that measure between 90 and 180 degrees, and <N can should be 64. The sum of 25, 64, and 91 is 180 degrees [25+64+91=180]. In conclusion, the Triangle Sum Theorem helps me determine whether three angles are the measuments of a triangle.