Proportionality Relationships
I.SectionObjectives
- Identify proportional segments when two sides of a triangle are cut by a segment parallel to the third side.
- Divide a segment into any given number of congruent parts.
II.Cross-curricular-ProportionalDivisions
- Have students participate in a hands- on activity to explore the section objectives.
- Students are going to work with several different triangles.
- The triangles should all be the same size.
- You can either prepare the triangles ahead of time or have the students cut them out themselves.
- Then have students work in small groups.
- In each group, the students are going to explore the proportional segments that are created when two sides of
a triangle are cut by a segment parallel to the third side. - They should try this will three different line segments each parallel to a different side.
- This means that the activity will get repeated with three different triangles.
- The students need to measure each side and write proportions to represent the different sections of the triangle.
- For example, when the triangle is cut, there are two polygons- how do the side lengths compare? Are they in
proportion? - Students need to make notes on these comparisons and share them with the other students.
III.TechnologyIntegration
- Use Wikipedia to explore the concept of proportionality.
- http://www.en.wikipedia.org/wiki/Proportionality
- Students can look at proportionality in mathematics, but also in human design and architecture.
- There are several different links to explore.
IV.NotesonAssessment
- Assess student understanding by observing their work in small groups.
- Were the students able to successfully cut the triangles into proportions?
- Were they able to write proportions that demonstrate that the two polygons are similar?
- Provide feedback as needed.
Similarity Transformations
I.SectionObjectives
- Draw a dilation of a given figure.
- Plot the image of a point when given the center of dilation and scale factor.
- Recognize the significance of the scale factor of a dilation.
II.Cross-curricular-Art
- The name of this activity is “Honey I Shrunk the Polygon!”
3.7. Similarity