Converse of the Pythagorean Theorem
I.SectionObjectives
- Understand the converse of the Pythagorean Theorem.
- Identify acute triangles from side measures.
- Identify obtuse triangles from side measures.
- Classify triangles in a number of different ways.
II.Cross-curricular-Architecture/Design
- Use the following image from Wikipedia to show students an image of St. Basil’s Cathedral.
- This is Figure 08.02.01
- http://www.en.wikipedia.org/wiki/File:RedSquareSaintBasile(pixinn.net).jpg
- You can either use this image as a discussion point or have students work with it in small groups.
- In small groups, have the students identify the equilateral and acute triangles in the cathedral.
- There are many of them to choose from.
- Then ask the students to identify how they know that these are equilateral and acute.
- The students should be able to discuss the different characteristics of what makes an acute triangle acute and
what makes an equilateral triangle equilateral. - Have students discuss this in small groups.
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III.TechnologyIntegration
- Ask students to research triangles and bridge designs.
- What is the most common type of triangle used in bridge designs?
- Why is it the most common?
- Have the students do some research on this and then report on their findings.
- Students should keep track of any websites they visit to refer back to when reporting on their findings.
IV.NotesonAssessment
- Observe students as they work.
- Listen to the discussions and you will hear whether the students have an understanding of acute, obtuse and
equilateral triangles. - Ask questions to expand student thinking.
Using Similar Right Triangles
I.SectionObjectives
- Identify similar triangles inscribed in a larger triangle.
- Evaluate the geometric mean of various objects.
- Identify the length of an altitude using the geometric mean of a separated hypotenuse.
- Identify the length of a leg using the geometric mean of a separated hypotenuse.
II.Cross-curricular-TriangularLodge
3.8. Right Triangle Trigonometry