Journal Journal: Consecutive Angle Theorem Skiers Instructions: 1.8.4 Geometry Honors Sem 1 Name: Date: Making the Slopes Safer for View the video found on page 1 of this journal activity. Using the information provided in the video, answer the questions below. Show your work for all calculations 1. The Students' Conjectures: (3 points: 1 point each) a. What conjecture is being made? Kayla's opinion is that angles cannot be calculated and must be measured. b. What key details are given? The sides of the down run are equal, so are the sides of the run. The angle of the existing fence is 35 degrees. c. What is your plan of action? Since the sum of the angles is 180, calculate the additional angle by subtracting 35 from 180 Journal: Consecutive Angle Theorem 1/5 1.8.4 Copyright © 2023 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use. Any unauthorized copying, reuse, or redistribution is prohibited. 2. Looking at the Consecutive Interior Angles (9 points) Look at the diagram of the scenario below. A steep downhill ski slope is intersected at an angle by a less steep ski slope. Safety fences need to be set up in the locations shown. The angles of the fences, angles 1 and 2, can be determined by finding the relationship between the angles a and b. a. Draw a geometric diagram of this scenario using two parallel lines and one transversal. (Remember that a transversal is a line which cuts across parallel lines.) Label the angles, parallel lines, and transversal as indicated in the diagram above. (2 points) It wont let me draw in google docs and i cannot draw it so i went on a 3rd party Journal: Consecutive Angle Theorem 2/5 1.8.4 Copyright © 2023 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use. Any unauthorized copying, reuse, or redistribution is prohibited. b. Starting with the fact that angles 1 and a are a linear pair and that angles b and 2 are also a linear pair, use a two column proof to prove that consecutive interior angles a and b are supplementary. (5 points) Statement Reason Statement:Angle 1 and a are a linear pair Statement: angle b and 2 are a linear pair Reason: They form a straight line and equal 180 degrees. This means that the interior angles are also supplementary. c. Explain what the result of your proof tells you about angles a and b. Specifically, if you measured one angle, what would you know about the other? (2 points) If you measure one angle, you can subtract it from 180 to find the second. They are both supplementary and consectuvite interior angles. Journal: Consecutive Angle Theorem 3/5 1.8.4 Copyright © 2023 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use. Any unauthorized copying, reuse, or redistribution is prohibited. 3. The Exterior Angles (6 points) a. The fences will be aligned with the exterior angles ∠1 and ∠2. What are some other relationships you can see between ∠1, ∠2, ∠a, and ∠b? (2 points) Angles 1 and 2 are supplementary Angles A and 2 are corresponding angles Angles B and 1 are also corresponding angles b. Which of the relationships you listed above will be the most helpful in figuring out the measurements of the safety fences? (2 points) Angle 1 and 2 are supplmentary c. What is the measure of ∠2? (2 points) 180 - 35=145 Journal: Consecutive Angle Theorem 4/5 1.8.4 Copyright © 2023 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use. Any unauthorized copying, reuse, or redistribution is prohibited. 4. Reflections (2 points: 1 point each) a. Can you think of any other real-life scenarios where parallel lines and transversals exist? Wind screen wiper b. What are the limitations of the ski slope scenario as a real-life example? In real life, ski slopes are not completely straight lines or geometric shapes. Copyright © 2018 Apex Learning Inc. Use of this material is subject to Apex Learning's . Any unauthorized Terms of Use copying, reuse, or redistribution is prohibited. Apex Learning ® and the Apex Learning Logo are registered trademarks of Apex Learning Inc. Journal: Consecutive Angle Theorem 5/5 1.8.4 Copyright © 2023 Apex Learning Inc. Use of this material is subject to Apex Learning's Terms of Use. Any unauthorized copying, reuse, or redistribution is prohibited.
