Geometry Task: Ratios, Proportions and Similar Figures

Geometry Task: Ratios, Proportions and Similar Figures

PDF icon Geometry Task: Ratios, Proportions and Similar Figures

Activity/Task Variations

Blooms taxonomy level: 
Understanding
Differentiation suggestions: 

If students can’t get started….
Assessing Questions:

  • Why did you use the Pythagorean Theorem?
  • How did you know that you could use the Pythagorean Theorem to solve this problem?

Advancing Questions:

  • Draw one diagonal on the square. What does the diagonal do to the square?
  • Do you see any shapes other than the square in your  figure?
  • What kind of triangle do you have?
Extension suggestions: 

If students finish early….

  • Ask students to go back through problems 2 and 3 using the longest side instead of the shortest side of the rectangle. Do the same types of conjectures hold? Why or why not?
  • Ask students to compute the ratio of the length of the shortest side to the length of the longest side for each rectangle they constructed in problems 2 and 3. Do the same types of conjectures hold for this ratio? Why or why not?
Originator: 
Tennessee Department of Education