Question

Nadia remarked that her figure has an infinite number of planes of symmetry. Jon gave a sly grin and remarked that his figure has an infinite number plus one! After explaining the difference between his figure’s planes of symmetry and hers, Jon convinces Nadia that his figure does have one more than hers. How might Jon have explained this?

Answer 1

Jon started with a diagram like the one below and drew a three-dimensional figure by rotating the circle 360° about line m.

Nadia started with a diagram like the one shown below and drew a three-dimensional figure by rotating the right triangle ABC 360° about line n.

· Name the three-dimensional figure created by each person.
· Nadia remarked that her figure has an infinite number of planes of symmetry. Jon gave a sly grin and remarked that his figure has an infinite number plus one! After explaining the difference between his figure’s planes of symmetry and hers, Jon convinces Nadia that his figure does have one more than hers. How might Jon have explained this?
Answer:
John’s figure:
Nadia’s figure:

Answer 2

Jon started with a diagram like the one below and drew a three-dimensional figure by rotating the circle 360° about line m.

Nadia started with a diagram like the one shown below and drew a three-dimensional figure by rotating the right triangle ABC 360° about line n.

· Name the three-dimensional figure created by each person.
· Nadia remarked that her figure has an infinite number of planes of symmetry. Jon gave a sly grin and remarked that his figure has an infinite number plus one! After explaining the difference between his figure’s planes of symmetry and hers, Jon convinces Nadia that his figure does have one more than hers. How might Jon have explained this?
Answer:
John’s figure:
Nadia’s figure: