Two- Column Proof
I.SectionObjectives
- Draw a diagram to help set up a two- column proof.
- Identify the given information and statement to be proved in a two- column proof.
- Write a two- column proof.
II.ProblemSolvingActivity-WindGenerators
- Use a figure like this one of a wind generator. This is Figure 02.06.01
- http://www.blaineschools.org/Schools/WRMS/Tech/Zsupportin_documents/Images/wind_generator.jpg
- Here is the problem.
- “Mike Eisele did an experiment for his science project to figure out which angle of degree on a propeller of a
wind generator would be the most efficient. He figured out that 75◦was the most efficient. Your task is to take
this given information and write a proof to using geometric principles. We’ll call one angle of the propeller
angle 1 and the other angle 2.” - Show students the diagram of the wind generator. Point out the two angles that you are working with and then
write this information on the board. - On Board:
Given:
m^61 = 75 ◦6 1 ∼= (^62)
Prove:m^62 = 75 ◦
III.MeetingObjectives
- Students will use a diagram to help set up a two- column proof.
- Students can draw a diagram of a wind generator and label the given angles.
- Students will write a two- column proof.
IV.NotesonAssessment
- Here is a possible answer for the given proof.
TABLE5.1:
Statements Reasons
m^61 = 756 1 ∼=^62 Given
m^61 =m^62 Definition of Congruent Angles
75 =m^62 Substitution
m^62 = 75 Symmetric Property- Observe students while they work. Offer assistance when necessary.
- If you want to learn more about Mike Eisele and his experiment, see the Enrichment section of this Teacher’s
Edition. The website about Mike and his experiment is http://www.share3.esd105.wednet.edu/mcmillend/02SciProj/ReeseC/reesec.html#Experimental
5.2. Reasoning and Proof