Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name: ___________________________________ Date: _____________ Transversals and Parallel Lines SCORE: _______/25 pts What does it Mean to be Parallel in both Geometry and Algebra? In Geometry, for two lines to be parallel, what two criteria must they have? In Algebra, for two lines to be parallel, what criteria must they have? Letβs investigate this to determine the answer: First β recall slope-intercept form: π¦ = ππ₯ + π 2 Equation of line: π¦ = 3 π₯ + 5 Draw TWO more lines that are parallel to the line given. Then determine the equation of both lines. The two lines that you drew, are they parallel to each other? Why or why not? (answer in complete sentences) In complete sentences, describe how you know that the two lines that you drew and the given line meet the criteria for Geometry. (May use the back if needed) Name: ___________________________________ Date: _____________ Transversals and Parallel Lines SCORE: _______/ 175 pts Investagation of Angles with Parallel Lines Part 1 β Following the four steps, complete the table, then answer the question(s): (10 pt) Step 1: Construct a line (cannot be vertical nor horizontal) and label two points on the line A and B. ** Every group members first two lines must have different slopes.** Step 2: Construct a line parallel to line AB. Label two points on this line C and D. (be sure to show lines are parallel on diagram) Step 3: Construct a transversal β‘πΈπΉ , label the points of intersection G and H respectively. Step 4: Use a protractor to measure each angle. (helpful hint β it might be easier if you make the lines extend really far) Write the angle measures in the chart below: (20 pt) Angle Your Measure Group Measure Group Measure Group Measure β π΄πΊπΈ β π΅πΊπΈ β π΄πΊπ» β π΅πΊπ» β πΆπ»πΊ β π·π»πΊ β πΆπ»πΉ β π·π»πΉ Here is an example of what your graph should look like, remember your lines do not have to go in the same directions as the example, but your points should be labeled the same way. Investigate the following: 1. Identify all six angle relationships pairs in the diagram 1. Then determine what conjecture, if any, can be made able their angle measures? (15 pt) Part 2 β On a separate graph, repeat the first four steps again, HOWEVER, this time, make sure that line CD is NOT PARALLEL to line AB. (30 pt) Angle Your Measure Group Measure Group Measure Group Measure β π΄πΊπΈ β π΅πΊπΈ β π΄πΊπ» β π΅πΊπ» β πΆπ»πΊ β π·π»πΊ β πΆπ»πΉ β π·π»πΉ 2. Identify all six angle relationships pairs in the diagram 2. Then determine what conjecture, if any, can be made able their angle measures? (15 pt) 3. Compare and Contrast the two diagrams. What happens with the angles relationships when lines are parallel vs. when lines are not parallel? What is the same in both situations? Why do you think this is true? Write your answers in a well-thought out paragraph, making sure you answer all questions clearly and correctly. (20 pt) APPLY WHAT YOUβVE LEARNED The blueprint contains many examples of the types of angle pairs you learned about this week and during this investigation, some formed by parallel lines and a transversal, and some formed by nonparallel lines and a transversal. Find the measure of ALL numbered angles in the blueprint. (2 pt) Record your measures in the table below: β 1 = β 2 = β 3 = β 4 = β 5 = β 6 = β 7 = β 8 = β 9 = β 10 = β 11 = β 12 = β 13 = β 14 = β 15 = β 16 = β 17 = β 18 = β 19 = β 20 = β 21 = β 22 = β 23 = β 24 = β 25 = β 26 = β 27 = β 28 = β 29 = β 30 = β 31 = β 32 =