- Look at each student’s triangles.
- Is the orthocenter of the acute triangle inside the triangle?
- Is the orthocenter of the obtuse triangle outside the triangle?
- Is the orthocenter of the right triangle at the vertex of the right triangle?
- Assess student understanding by assessing each individual triangle.
- Offer feedback/correction when necessary.
Inequalities in Triangles
I.SectionObjectives
- Determine relationships among the angles and sides of a triangle.
- Apply the Triangle Inequality Theorem to solve problems.
II.ProblemSolvingActivity-ProvetheTheorem
- In this problem, students need to use the information given to draw a diagram and prove the theorem.
- Students are going to prove the theorem that states that the angle opposite the longest side of a triangle with
unequal sides will have the greatest measure. - Here is the problem.
- “In triangleABC,AB<BC, the measure of angleAis 80◦. The measure of angleCis 40◦, and the measure of
angleBis 60◦. Given the theorem on side lengths and angle measures, can this be a true statement? Why or
why not?” - Provide students time to work on this problem.
- Students need to provide a diagram, a written explanation and a verbal explanation to explain their thinking.
- When finished, allow students time to present their work to the class.
III.MeetingObjectives
- Students will determine relationships among the angles and sides of a triangle.
- Students will apply the Triangle Inequality Theorem to solve problems.
- Students will demonstrate understanding through diagrams, written explanations and verbal explanations.
IV.NotesonAssessment
- Here is the solution to the problem.
- This is a true statement because the length ofBCis longer thanAB. The angle oppositeBCis the greatest of
the three angles in the triangle. It measures 80◦. Therefore, the theorem is accurate and proven through this
statement. - Be sure that the students have diagram that resembles Figure05.06.01
- Offer feedback and correction when necessary.
Inequalities in Two Triangles
I.SectionObjectives
- Determine relationships among the angles and sides of two triangles.
Chapter 5. Geometry TE - Problem Solving