Upload
mae-bennett
View
218
Download
1
Tags:
Embed Size (px)
Citation preview
Chapter 1
Using Geogebra
Doing Mathematics
• Geogebra Dynamic Easier to see what happens to geometric
objects
• Make observations
• Formulate conjectures If … [hypothesis] … then … [conclusion]…
Conjectures
• Hypothesis Assumptions
• Conclusion What happens when assumptions hold
• Often expressed using If … then …
Conjectures
• Ask yourself What is happening Why is it happening What properties of figures made it happen
Geogebra Tips
• Straight edge tools
Geogebra Tips
• Polygon tools
Geogebra Tips
• Circle tools
Geogebra Tips
• Changing object property – color
Geogebra Tips
• Using arrow tool Drag a point, view results
Geogebra Tips
• The Point tool Use to establish an intersection
Observing, Conjecturing
• Inductive reasoning Examine examples Discover patterns
• Deductive reasoning Justify the conjecture Find explanation why conjecture holds Proof
Language of Geometry
• Formal definitions Precision necessary Math definitions are prescriptive
• Definition different from properties Example: define rectangle Construct figure only with definition
Polygons
• Closed figure In the plane Formed by set of line segments Each segment shares each endpoint with
exactly 1 other line segment
• Poly - many
• - gons angles
Quadrilateral
• Joining midpoints of arbitrary quadrilateral?
Quadrilateral
• Self intersecting polygon
Quadrilateral
• Concave polygon
Viviani’s Theorem
• What was the sum of l + m + n? What if P was outside the triangle? What if the triangle was not equilateral? What if it
is a square?
P
Family of Quadrilaterals
• Identify the categories
Angles Inscribed in Circles
• What relationships did you find?
Rules of Logic
• Statements … open? closed? true? false?
All cars are blue. The car is red. Yesterday was Sunday. Rectangles have four interior angles. Construct the perpendicular bisector.
Rules of Logic
• Use logical operators and, or
• Evaluate truth of logical combinations
P and Q
Rules of Logic
• Combining with or P or Q
Rules of Logic
• Negating a statement not P
Chapter 1
Using Geogebra