Taxicab Geometry

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# Taxicab Geometry - PowerPoint PPT Presentation

Taxicab Geometry. TWSSP Tuesday. Welcome. Grab a playing card and sit at the table with your card value Determine your role based on your card’s suit. Tuesday Agenda. Agenda Refresh Euclidean definitions

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### Taxicab Geometry

TWSSP Tuesday

Welcome
• Grab a playing card and sit at the table with your card value
Tuesday Agenda
• Agenda
• Refresh Euclidean definitions
• Given constraints on relative distances, determine the taxicab sets of points satisfying those constraints
• Establish and explore ideas of taxicab congruence
• Question for today: How do common Euclidean definitions of figures and congruence compare to corresponding definitions in taxicab geometry?
• Success criteria: I can …
• Find sets of points taxicab and Euclidean – equidistant to two points
• I can plot, define, generalize, and describe properties of a taxicab-circle
• I can define, and make use of taxicab- congruence
Taxicab and Euclidean distances
• Under what conditions on points A and Bdoes

dT(A, B) = dE(A, B)?

• For any two points, how do the taxicab and Euclidean distances between the two points compare?
What do we know?
• Use the Think (5 min) – Go Around (5 min) – Discuss (10 min) protocol
• What is the Euclidean definition of equidistant?
• What is the Euclidean definition of a circle?
• What is the Euclidean definition of an equilateral triangle?
• What is the Euclidean definition of a square?
• What does it mean for two line segments to be congruent?
• What does it mean for two figures to be congruent?
Midsets
• A midset is the set of all points equidistant between two points.
• Find the taxicab and Euclidean midsets for the maps provided using a Think – Go Around – Discuss protocol
• When are Euclidean and taxicab midsets different? Why?
Fixed distances
• Complete the activities on the Fixed Distances sheet, using the Think – Go Around – Discuss protocol
• How would you describe the boundaries of the regions you found?
Taxicab Circles
• I notice/ I wonder about taxicab circles (at least 2 of each)
Taxicab Congruence
• Think – Go around – discuss: What would need to be true in order for two line segments to be taxicab-congruent?
• What would need to be true in order for two figures to be taxicab congruent?
Taxicab Triangles
• It can be shown that taxicab geometry has many of the same properties as Euclidean geometry but does not satisfy the SAS triangle congruence postulate.
• Find two noncongruent right triangles with two sides and the included right angle congruent
• Explore taxicab equilateral triangles. What properties do they share with Euclidean equilateral triangles? How do they differ?
Exit Ticket (sort of…)
• When will taxicab and Euclidean midsets between two points be the same? When will they be different?
• Suppose you have a taxicab circle of radius 3 centered at (0, 0) and a Euclidean circle of radius 3 centered at (0, 0). List everything that the two circles will have in common, and everything that will be different about them.
• If two triangles are Euclidean congruent, will they be taxicab congruent? Explain.
Cognitive Demand Framework
• Memorization
• Procedures without connections