- Apply the SAS and SSS Triangle Inequality Theorems to solve problems.
II.ProblemSolving-NamethatInequality
- This problem solving activity is a game.
- Preparation is to prepare two Congruent Triangles for each group to work with.
- Students play it in groups of four. In the groups of four, they split up into pairs.
- Each pair is a team that plays against each other.
- When the students play, they are trying to “stump” the other party.
- The play begins like this, one team comes up with a problem for the other team to solve.
- For example, “If I lengthen sideABwhat inequality compares sideABtoCD?”
- Then the other team has to answer it.
- If they answer it correctly, the team receives a point.
- If not, the other team gets a point.
- Then they repeat the process by switching team positions.
- Both teams play until time is up.
- Students need to be encouraged to use the SAS Triangle Inequality Theorem and the SSS Triangle Inequality
Theorem as well as the converse Theorems. - Students can create as many different types of questions as they would like.
- Students can be very creative in their approach to writing questions.
III.MeetingObjectives
- Students will determine relationships among the angles and sides of two triangles.
- Students will apply the SAS and SSS Triangle Inequality Theorems to solve problems.
- Students will demonstrate their knowledge and understanding through the quiz game.
IV.NotesonAssessment
- Walk around as students play and assist students when necessary.
- Offer suggestions and challenge students to create difficult questions.
- Notice which students are having difficulty with the assignment and offer assistance and coaching.
Indirect Proofs
I.SectionObjectives
- Reason indirectly to develop proofs of statement.
II.ProblemSolvingActivity-DrawitOut!
- Assign students the task of drawing an example of a geometric proof and an algebraic proof.
- Tell the students that they are going to use indirect reasoning to develop these proofs of statements.
- Here is one possible example for an algebraic problem.
- “Marcy is selling candy bars for the school band. She starts out selling five bars. But in the end, she sells three
times as many as her friend John does. The band teacher congratulates her on selling over forty candy bars. If
John sold less than 12 bars, Marcy did not sell more than forty bars.” - Students need to write a proof to show this statement is true.
- Here is the answer:
5.5. Relationships within Triangles