MLS                                                                                                Yolanda Volcimus
Harvard                                                                                             10/21/12


      Prompt: Discuss what you have learned about the angles formed when two parallel lines are cut by a transversal. Describe the special angle relationships that appear, and how are they related to each other. Last week, you learned about complementary and supplementary angles. Discuss how these angle relationships do or do not play a role within the parallel lines and transversal. Finally, where might you see parallel lines cut by transversals in the real-world? How might knowing the angles location to each other help you in these real-world scenarios?

       Answer: In class, I've learned about angles formed when two parallel lines are cut by a transversal. I've learned the special angle relationship that appears and how they are related to each other. I also learned about Complementary and Supplementary angles and how they play a role within the parallel lines and transversal. Finally, I might see parallel lines cut by transversal lines in real-world. Knowing the angles location to each other might help me in these real-world scenarios.
          Parallel Lines are lines in a plane that never meet or interact. However, a Transversal is a line that intersects two or more lines that lie in the same place. Transversal to parallel lines form angles with special properties. These angles are called Alternate Exterior and Alternate Interior Angles. Alternate Exterior Angles is when two parallel lines are cut by a transversal and the two pairs of angles on opposite sides of the transversal and outside of the parallel line. Alternate Interior Angles is when a transversal crosses two parallel lines and each pair of these angles are inside the parallel lines, and on opposite sides of the transversal. These two angles are related to each other because they both work together to give us a better understanding of angles in parallel lines cut by transversals. 
        Complementary Angles are two angles whose sums equals to 90 degrees. Whereas, Supplementary Angles are two angles whose sums adds up to 180 degrees. Supplementary Angles play a role within the parallel lines and transversal because whenever there's a transversal in two parallel lines, the two angles will form a Supplementary Angle. Nevertheless, two parallel line cut by a transversal will never provide a Complementary Angle. I see parallel lines cut by transversal lines in real-world in places like a window. Knowing the location to each other might help me in these real-world scenarios because I can know whether tha angles are congruent angles or corresponding angles.
                                

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. 

                                                       

          

MLS                                                                                             Yolanda VolcimusHarvard                                                                                        10/11/12         Prompt: What does it mean when you see the phrase “Not Drawn to Scale” next to a geometric image? What might happen if you use a measurement tool to solve this type of problem? When an image in not drawn to scale what is the best strategy one can use to solve the problem?

       Answer: When you see the phrase "Not Drawn to Scale" next to a geometric image, this means that the image is not drawn exactly the right size or the picture is not actually accurate. If you use a measurement tool to solve this type of problem, you will get the problem incorrect. The best strategy you can use to solve a problem that is not drawn to scale is to utilize mathematical principles to determine the answer based on the given measurements. You should also use the formula to solving the problem according to the given measurements. Thus, the phrase "Not Drawn to Scale" next to a geometric image is really important to consider when solving a mathematical problem. 

MLS                                                                                                   Yolanda Volcimus
Harvard                                                                                                10/1/12


           A single transformation that can replace the combination of a reflection across the y-axis followed by a reflection across the y-axis is a 180 degrees counter-clockwise rotation. These translations are equivalent because they both have the same coordinates; same size and shape. A=(1,3), B=(2,1), and C=(1,1); A''=(-1,-3), B''=(-2,-1), and C''=(-1,-1). After performing the 180 degrees counter-clockwise, my coordinates were: A'=(-1,-3), B'=(-2,-1), and C'=(-1,-1). Knowing that two reflections are equivalent to one transformation can help me to remember the rule for the single transformation because I know that a reflection over the y-axis will get the image in the 3rd quadrant if the image was in the first quadrant. Also, a 180 degrees counter-clockwise rotation will get the image in the 3rd quadrant if the image was in the first quadrant. Thus, two transformations can be equivalent to one transformation.