Trapezoids
I.SectionObjectives
- Understand and prove that the base angles of isosceles trapezoids are congruent.
- Understand and prove that if base angles in a trapezoid are congruent, it is an isosceles trapezoid.
- Understand and prove that the diagonals in an isosceles trapezoid are congruent.
- Understand and prove that if the diagonals in a trapezoid are congruent, the trapezoid is isosceles.
- Identify the median of a trapezoid and use its properties.
II.ProblemSolvingActivity-TrapezoidalTowers
- In this problem, the students are going to have to use what they have learned about trapezoids to justify why
or why not a tower characteristic is an isosceles trapezoid or a non- isosceles trapezoid. - Here is the problem.
- “Jonas is studying architecture. He is really interested in unique geometric architecture. Jonas decides to share
two of his favorite buildings with his friend Sam. One is of the Shanghai World Financial Center and the other
is of Sutton Place in NYC. Jonas looks at the two towers and says, “It’s a shame that the hole in the top of
the Shanghai World Financial Center isn’t an isosceles trapezoid like Sutton Place that would be really cool.”
Sam looks puzzled.” - Figure 06.07.01 http://en.wikipedia.org/wiki/Shanghai_World_Financial_Center
- Figure 06.07.02 http://www.thecityreview.com/sutton/rivtow.html
- Look at each building. Why does Jonas think that the hole in the Shanghai World Financial Center is not an
isosceles triangle? Use what you have learned to help Sam understand. - Students need to use a written explanation and diagrams to complete this problem.
III.MeetingObjectives
- In completing this problem, the students will use the properties of isosceles and non- isosceles trapezoids.
- Students will use the Base Angles Theorem.
- Students will write out and justify their answers.
IV.NotesonAssessment
- Read student answers and look at student diagrams.
- Were they able to see that the base angles of Sutton Place are congruent?
- Were they able to see that the opposite sides of the Shanghai building are not congruent?
- Is student writing clearly written?
- Are there diagrams to illustrate student understanding?
Kites
I.SectionObjectives
- Identify the relationship between diagonals in kites.
- Identify the relationship between opposite angles in kites.
II.ProblemSolvingActivity-Let’sGoFlyaKite!
Chapter 5. Geometry TE - Problem Solving