Geometry, Teacher\'s Edition

• Possible answers could be:^6 1 and^6 2 are vertical angles. Vertical^6 ’s are congruent.


• Here are the three other starters:^6 1 and^6 4 are supplementary angles.
  -^6 3 and^6 4 each equal 55◦.
  -^6 2 and^6 3 are adjacent angles.
  -^6 3 and^6 4 are congruent.


• Finally, when finished, ask students to identify whether the Law of Detachment or the Law of Syllogism was
  at work in each set of statements.

III.MeetingObjectives

• Students will use the basic rules of logic.


• Students will understand the role of inductive and deductive reasoning.


• Students will apply this reasoning to geometric content.

IV.NotesonAssessment

• Observe students as they work.


• If groups are struggling, refer them back to their notes on previously learned material.


• Refrain from offering suggestions.


• Give feedback based on content and accuracy.

Algebraic Properties

I.SectionObjectives

• Identify and apply properties of equality


• Recognize properties of congruence “inherited” from the properties of equality


• Solve equations and cite properties that justify the steps in the solution


• Solve problems using properties of equality and congruence

II.ProblemSolvingActivity-MatchItUp

• Students are going to create a matching game that they can then play in small groups.


• Each small group needs to create a pair for each of the properties. One card will have the name of the property
  on it, and the match will be a numerical example, and or a geometric example.


• Be sure that the students write out an actual example of the property and not just variables as they did in class.


• This will help them to take the lesson in the text to a new level.


• Be sure that the students have index or small cards, pens, rulers, etc.


• After the cards have all been created, have one group exchange with another group and play that team’s game.


• When finished, ask the teams to give each other feedback on the examples used.


• Here are the properties to use:
  
  
  • Reflexive Property
  
  
  • Symmetric Property
  
  
  • Transitive Property
  
  
  • Substitution Property
  
  
  • Addition Property of Equality
  
  
  • Multiplication Property of Equality
  
  
  • Reflexive Property of Congruence with segments and angles
  
  
  • Symmetric Property of Congruence with segments and angles
  
  
  
  

5.2. Reasoning and Proof