Geometry Sem 1 (S2444116)
Points possible: 20
Making the Slopes Safer for Skiers
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?
Managing the flow of downhill skiers for potential accidents
b. What key details are given?
A drawing the two ski slopes, the angles between the two slopes
c. What is your plan of action?
Use the parallel lines to determine the angle of the other slope
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)
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 the relationship between a and b, which are consecutive interior angles. (5 points)
Statement Reason A II B 2 II lines cut by a transversal
c. Explain what the result of your proof tells you about intersecting ski runs. (2 points)
3. The Exterior Angles (6 points)
a. The fences will be aligned with the exterior angles ∠1 and ∠2. What are some