3.5 Relationships Within Triangles
Midsegments of a Triangle
I.SectionObjectives
- Identify the midsegment of a triangle.
- Apply the Midsegment Theorem to solve problems involving side lengths and midsegments of triangles.
- Use the Midsegment Theorem to solve problems involving variable side lengths and midsegments of triangles.
II.Cross-curricular-Mapping
- Use the following image of the Bermuda Triangle in this activity.
- This is Figure 05.01.01
- http://www.en.wikipedia.org/wiki/File:Bermuda_Triangle.png
- Each student will need a copy of the image to work with.
- Use a scale and a ruler to determine the distance between each of the vertices of the triangle.
- Then determine the midsegment of the triangle.
- Draw the midsegment into the image of the triangle.
- After drawing in the midsegment, write a proof that proves that this is the correct midsegment of the triangle.
- Students can work on this in pairs so that they have peer support when writing the proof.
- Students may want to name each of the vertices to help with writing the proof.
- When finished, allow time for the students to share their work.
III.TechnologyIntegration
- Use Wikipedia or another website to research facts about the Bermuda Triangle.
- What are some of the mysteries surrounding this area?
- When was it discovered to be a “triangle” in shape?
- Be prepared to share your findings with the others in the class.
IV.NotesonAssessment
- Assess student understanding by examining the proof.
- Is it clear?
- Is the given information clear?
- Is it clear which information needs to be proven and which does not?
- Provide students with feedback on their work.
- Share strong example with the others in the class so that all can improve their proof writing.
Perpendicular Bisectors in Triangles
I.SectionObjectives
3.5. Relationships Within Triangles